Sigh,

Welcome to America. The whole concept of service agreements, etc. is to get your $$ without providing anything in return. If you have a catastrophic failure, engine, trans, etc. they're worth it, maybe. Consider all the "stuff" around your estate and if you'd bought an agreement for all of it....

My Sears story. I bought a GT500 about 10 years ago and as we were moving, building a house and barn, etc. I didn't have time or interest in fooling with a tractor that I planned on using for a ton of things so bought the agreement. After a few months thought it was running rough, so called for service. The guy came out and said, you have a bad plug and that's not covered. HUH? 3 month old tractor, it had the "long life platinum plugs," etc. He then laughed and said I'm supposed to say that, but here's the new plug and I'll write it up as something else. Good Guy. Read the Small Print in your agreement, they're probably right in "customer responsibilities" cover batteries. The service agreement did pay for itself as I ended up getting TWO new engines. This was during the Briggs air cleaner fiasco a few years back.

'were I you, I'd take the battery out and take it to Autozone or equivalent and have it load tested. If it's good, call sears, if it isn't buy a battery.

Good luck,

Ev

You did the right thing by refusing to try what you say she was suggesting.
Either YOU misunderstood verbatim what she was attempting to tell you.................or she was pretty far off the mark regarding what she should have been saying...........because the procedure as you stated it here would not have proved anything.
DIY repairs can be a mix of rewards and consequences. The rewards can be a significant savings of money and the satisfaction of having accomplished the work yourself.
The consequences can range from completely botching the work to serious personal injury if things go awry.
Messing with batteries is an area where things can go awry in an instant if a person is not well versed in the basics of battery handling safety.

The part about "being charged for a service call" is just one of the caveats of buying extended warranties or service plans. In this case the main problem is likely a dead battery.......and I doubt their plan covers boosting (or replacing) dead batteries.
Their plan "might" cover repairs to the tractor electrical CHARGING SYSTEM (but not the battery) if a defect therein is the cause of the dead battery.
The most likely issue with your tractor battery right now is that it is at least 2.5 years old (maybe much older) and has simply worn out. Average battery life in this class is about 3 years.
Also not likely covered by their plan would be if the clicking sound you describe is due to an engine that might need a routine valve adjustment to ensure its compression release feature is functioning properly to allow for easy cranking. You did not include the Craftsman model number or name the brand of engine so I can't tell if your engine might possibly need that routine service. The bottom line in that thought is that if the engine DID need a valve adjustment to affect a working compression release........it would be on your bill because that is defined as routine maintenance........not a defect.
The sales personnel describe these plans to be "all encompassing" but they often fail to describe what that actually means in a lot of cases.

Is she aware of the potential explosion from hydrogen gas when jumping a battery?

Likely, you battery needs to be charged after sitting over the winter, but...

It can be confusing to tell the difference between a maintenance agreement and an extended warranty for manufacturing defects when one buys them especially if one doesn't know the difference and/or doesn't read what they are buying before they plunk down their money.

Sears offers both for their L&G products.

My good frriend and neighbor who lived a few houses away from me, would always have me do the spring cleanup and "get-ready" work on it, for which i would charge a paltry sum, and all was good.
And then, he died! And his widow, who always thought i was a chiseler and charged too much, called Sears to come out and do the spring go-round. They did, and charged a lot of money. After the repair man left, and the next time she mowed their grass, she noticed that the deck wasn't level! Now, it had never been out of line before the advent of the Sears Mechanic, so i checked the deck levelling stuff, and found one side too low! And also, evidence of tool marks. I set both sides as level as i could, and the next time she mowed, the grass looked level. I think the repair guy messed with the deck adjustments, figuring he'd get another expensive repair job! JMHO:RJ

OP, here: after reading all your responses, I decided to take out the battery, bring it to my local mower repair shop, and since it was dead (with no hope of resurrection), have it replaced. Mower works fine! I paid 2x what I should have for the battery --- so I learned two lessons.

BTW: despite its small size, I was as intimidated by that battery as by the monster in my Benz. I wore rubber gloves and acted like everything was explosive ... but the deed is done.

After being a Sears customer for more than 40 years, I have vowed to never buy another thing from them.

Both the battery in your Benz and the battery in your lawn tractor have enough sulfuric acid in them and enough electric capability to do serious damage to the vehicle and you. Wet lead acid batteries of any size should always be treated with respect.

To do anything one must have the knowledge and the tools. Lacking either usually results in bad things happening sooner or later. Wise people know what they know and know what they don't know. There's nothing wrong with paying someone to do something for you that you don't know how to do regardless of the criticism of those who are stupid enough to attempt anything regardless of the consequences.

Now that you have a fresh battery in your rider you should check the charging system or have it checked to make sure that a dead battery was the disease and not just a symptom.

*****Is she aware of the potential explosion from hydrogen gas when jumping a battery? *****

While this is a possibility, the chances of an explosion with the mower and a car is in an open area with the hood up is low.

Basically you connect the positive to the positive and the negative to the negative poles on both batteries. Care must be taken to not cause the sparks when you are connecting the batteries. There are some opinions as to which should be first but the both can spark if done incorrectly.

If you are not confident ask either your tractor or car service man to give you a demonstration of how to make the connection.

Hydrogen which could be generated by the battery is lighter that air. If in the open and there is some air moving there will be no place for the Hydrogen to collect to create an explosive mixture of air (oxygen) and hydrogen.

I have been doing this for years and am ready for all of the environmentalist and other experts to tell me I am wrong

"Basically you connect the positive to the positive and the negative to the negative poles on both batteries" and that's where you are wrong and should NOT be instructing those less knowledgeable on how to do it wrong.

"I have been doing this for years and am ready for all of the environmentalist and other experts to tell me I am wrong". Glad you're ready cause here it comes...

The correct way to jump from an installed car battery is positive to the positive on both batteries and negative from the car battery to an engine ground on the other end. Connecting the proper way almost completely eliminates the possibility of an explosion. You don't know what you don't know.

The difference between you and the OP jumping an LT with a car is that you have some knowledge and some experience where the OP knew they did not.

Ignorance can be cured but stupidity is a lifelong affliction.

I go pole to pole when jumping cars. It is hard to find a good ground otherwise. Yes, it is the proper way to do it, but impractical in reality. If you are worried about hydrogen buildup, take the caps off.

"I go pole to pole when jumping cars. It is hard to find a good ground otherwise"

Yup, sure is hard to find a ground under the hood of a car cause there's no alternator brackets, no power steering brackets, no head bolts, exhaust manifold bolts, and never a chassis to engine ground on the inner fenders and/or firewall. Good grounds are right under your nose if you take the time to look.

"If you are worried about hydrogen buildup, take the caps off" and that's begging for an explosion. It is the hydrogen that ignites so opening the caps gets the spark to it quicker and easier.

I have a set of "safety booster cables" that I bought way back in the '80s. These jumper cables separate into 2 halves at a heavy duty polarized connector located mid span. When separated, 1 cable pair has a male connector and the other pair is female. Each connector has a red & a green LED.
If you have connected the alligator clamps according to the correct polarity at the battery.......the green LED is lit. If you have it backward, the red LED is lit.
With these cables you connect 1 cable pair to each vehicle first. After you are seeing both green LED's lit, you then plug the 2 mid span connectors together to complete the transfusion.

Those cables achieve the same objective as hooking the last negative to an engine ground. The final cable connection that might spark is NOT at either battery.

Precisely, and that is why they were marketed as "Safety Booster Cables".
Even though the cables can be connected directly to BOTH battery posts safely when used as designed..........I always connect them (and all booster cables) in the prescribed safe manner of making my last connection of the negative clamp to a suitable chassis or engine ground away from the "dead" battery. I always check for a green LED to be present as confirmation of correct polarity match.