In the stain removal area of the cleaning section of your favorite box store or grocery store, they have a lot of different options for cleaning dye out of clothing that wasn't supposed to be there. (if you know what I mean)

I have used a product called "brite white" on a couple of things that have had dye depositted on them, with pretty good success. If you look, I think Rit has a product with dye remover in it as well. If all else fails and you are going to throw them out anyway, you could bleach them. It doesn't seem to hurt lime green as much as some other colors. My SD's favorite color seems to be lime green. So with softball practice and the stuff she picks up riding bikes, I get more than a little practice cleaning it.

Good luck.

Thanks, Peanutmom! I'll look for Brite White at the store. I was afraid Rit dye remover might remove the lime green?

The dye remover might lighten the lime green, but it seems like this is a color that seems to take a lot of abuse and not show it so much. Anything that works, sometimes, to save a favorite item.