are they white sheets per chance?

No the sheets are a soft aqua. So I can't try bleach.

However, today is a gorgeous cool sunny day.

Would drying outside in the sun help naturally bleach out the stains?

If sheets are "colorfast"...
You actually can use bleach on colors (l've done it successfully),
You just can't use too much and you need to dilute it before the clothes are added.

If your using an old fashioned top loader, fill it with water with no sheets (warm or cool), add 1/4 cup bleach and let agitate a minute, then add sheets and let run through a short cycle (9-6 minutes) with normal agitation.

You don't need to use detergent for either method.

If using a HE top loader or front loader (if you can) let machine fill with warm or cool water, pause machine, add 1-2 teaspoons of bleach to water, let agitate a minute, pause, then add sheets and run through short cycle.

I've done this with black dockers to kill a musty smell and it worked with no issue.

Just don't let bleach come in contact with sheets, it must be diluted first.

No the sheets are a soft aqua. So I can't try bleach.

However, today is a gorgeous cool sunny day.

Would drying outside in the sun help naturally bleach out the stains?

I used a very moderate concentration of bleach (soaking the entire shirt in our old top loader washer) on a favorite beige shirt that somehow got a vivid green stain on it (seems my wife messed up during the previous washing) and after soaking for an hour it was still there, so i put it back into the bleach/water for another hour and the stain was still prominent. Since the shirt was unwearable with the stain, I figured what the heck, and left the shirt to soak for a total of around six HOURS and lo and behold the stain was gone and the beige shirt remained virtually unchanged in color. Not only that, but the fabric (knit) wasn't damaged at all.

Not saying that you will be so lucky, but your options are limited at this point.

actually u have another option. return the sheets since the packaging was the issue. if they had used something that couldn't transfer color if one accidentally left it with the sheets during the first wash none of this would have happened. i wouldn't be bashful about asking for an exchange.

dave1812 wait a minute...

Are you saying the store has to eat the loss of the sheets because the user didn't totally check the sheets that they physically took out of the package and put into the washer (with the cardboard)?
How is that the stores fault? It's not even the sheet manufactures fault.

Either the user has to deal with the cardboard stuck/stained and try to fix it or go out and get another set of sheets and NOT make the same mistake again (at their own cost).

It WAS a mistake on the CUSTOMERS end nobody elses.

Hot water will set a stain. So if you soaked first in hot water that's likely why the stains aren't coming out.

I would use the sheet as is. Each time, before washing, soak the stained sheet overnight with Oxiclean in COLD water. Then wash.

Over time it may help remove the stains. Chlorine bleach will very likely remove the color. I don't know what someone is thinking when they suggest soaking aqua sheets in chlorine bleach. It's like 1922.

@dave1812

I'm not on my high horse (it's knowing where to draw the line).

It's one thing when manufactures make big mistakes and expect you (the consumer) to "deal" with your decision to purchase their products and do nothing about it when a product fails due to manufacturing or defective parts.

But it's another when an honest mistake is made by the consumer that looks to point fingers at everyone else and expects everyone else to compensate for their own error.

My mother raised me to be responsible for the errors of my ways and not hold someone else responsible.

I'm sure either the store or manufacture would "be happy" (not really) to reimburse or replace the sheets because this is unfortunately the world we live in now.
Where people think everything is someone else's fault.
When in fact we are sick of dealing with you and the complaining and just want you out of the store.

Personally I would suck it up and chalk it up to a lesson learned and not make that mistake again.

That is what jockewing is doing here, trying to get legitimate help on removing a stain they accidentally caused.
Jockewing isn't looking for a hand out but a solution.

By the way jockewing, has the staining lightened up any?