Thanks everyone for continuing to provide hints here. I'm still learning what works for me, going slowly and trying different things. :-) I am able to tear away the top decorative surface, as fnmroberts says, so I did that first for a small section, and then taped the plastic as christophern said. For soaking, I had been using a small sprayer and sponge method first, then tried a little Dif (gel) to see if that was easier than the hot water/fabric softener solution. (And I happened to have some of that Dif on hand). No clear winner: the Dif doesn't drip as fast as the water does, but I seem to use too much Dif to get the same peelability--and the water mixture is cheaper. :-) My dad suggested to "paint" the Dif on instead of simply spraying it on, and I might try that as an experiment. I don't mind going slowly and experimenting, as I'm learning as I go. I'm going to have to do more of the house down the road, so might as well practice until I know what works for me. My dad thinks I should rent a steamer and get it done asap, but I think then the floors really would get wet! Thanks again for the tips on protecting the floor!

The peanut butter and veggie oil mixture sounds like a safe bet. It has worked well for me in the past. Another approach is to use WD-40 but you would want to test it on the surface before you go all out. A bit on a rag would be the way to start. I used it on some adhesive residue where my hardwood floor comes up against marble and it worked well and did not harm the wood.

Hardwood throughout my entire first floor, including the kitchen and all entry areas. Residents don't wear shoes in the house. Human residents, nor furry ones. :) Visitors are not given any rules upon arrival. :) Most people see you walking around in bare feet, or socks, or slippers, and immediately move to take off their shoes. Depending upon who they are and why they are there, I often tell them don't bother. For instance, if it's the HVAC guy and he's going to work in the cellar, I couldn't care less if he keeps his shoes on. As someone noted upthread, the nice thing about hardwood is that it does clean up very easily. I prefer the residents keep shoes off the floor b/c it does keep the floors cleaner, but there is no way I would ever make a guest remove their shoes. As far as damage - most of the damage to my floor comes from the toenails of the 20 pound furry lunatics who share my home. Yes I keep them short - no lectures on appropriate dog nail procedures please! They are young and love to run and play - nails dig in on cornering no matter how short they are. :) However there has been some damage from people in shoes who had rocks stuck in the treads. Most of it from the early days when the house was under construction because sadly my GC was an inconsiderate moron regarding things like this. TL:DR. It's hardwood. It dents. I do what I can to keep the dents to a minimum but don't stay up at night about it either.

We have dark Mohawk engineered wood floors and have same chipping/peeling issue. Floor wasnt even 6 mos. old and started in high traffic areas. Its the thinner board so you cannot sand down. Its as if paper thin particle board was painted with with a cheap stain. Its an absolute garbage floor and was a huge mistake in retrospect going for aesthetics vs higher quality. Home was built with 3/4” hardwood flooring prior and we went for the more affordable ’new thing’. Lesson: don’t get seduced by the look and do NOT skimp on flooring.