Removing dye stains from wall?

Actually, dye can be really permanent. Is the wall papered or painted? If it's painted, first give it a little scrub. Be careful to only scrub the stains if the paint is not glossy. Perhaps you could touch up over with fresh paint, using a little brush.

If it's papered and the wallpaper doesn't have a vinyl finish, you shouldn't even try to scrub. There's nothing you can do unless you have leftover wallpaper to patch it with, in which case you would carefully cut out the damaged section, remove it by softening the paste with a small sponge. This may take a while, be patient, and try not to get the rest of the paper wet. Then you would need to cut an exactly matching patch. Talk to a wallpaper store about proper adhesive for this type of repair.