I just discovered that an OLD bottle of Avon skin so soft, I've had it for many years, does a stellar job of removing permanent ink from plastic. I tried it because it also works for removing sticky label remains, and ants will not cross over an area that has just been wiped with it. Amazing stuff! Just put a dab on a paper towel and rub. I wonder what else it is good for.
You can remove permanent marker on plastic using a nail polish remover, Mr. Clean Magic Eraser, baking soda toothpaste, rubbing alcohol, or hairspray (the cheaper the better). Just cover the marker stain with the product you have chosen, let it set for several minutes, and then wipe the surface clean. After this, repeat if it is necessary. Read more on www.howtocleanstuff.net/how-to-clean-permanent-marker/.