Put on a pair of gloves and a breathing mask. Pour ammonia into a small bowl. Toss in a few cotton balls, and allow them to become saturated with the ammonia.
Wipe the dye off the wall with the ammonia-soaked cotton balls.
Rinse the wall with a wet washcloth. Dry it with a lint-free towel.
Scrub the wall with a wet magic eraser, if any dye remains. The magic eraser is a soft sponge, so it won't damage the paint.
Cover the dye stain with a color run remover, if any dye remains. Color run removers are usually made for clothing, but they can work on your wall.
Combine 1/2 cup of borax with 1 gallon of hot water. Scrub the painted wall with the solution. Dry the wall with a lint-free towel.