While it's never easy to remove permanent marker, there are some things you can try. This is a guide about removing permanent marker from plastic.
How can you remove Sharpie permanent markers stains from plastic headlamp lenses?
By Jeremy from Richmond, VA
I wouldn't use nail polish remover on plastic.I'd try something like WD40.
I would try rubbing alchohol first. Do a "test" on a corner to make sure it won't cloud the plastic, but I think it will not.
Try Oops or GooGone.
I have had luck removing Sharpie ink with regular isopropyl alcohol from the grocery store or any drugstore chain. It doesn't harm most surfaces, and usually takes all the ink off.
How to remove sharpie marker off the back of a TV?
Sakeitha from TX
There is a product at the supermarket called "Magic Eraser" from Mr. Clean. It takes off anything, including Sharpie Marker marks. My son decided to write on several walls with a green sharpie and it all came off with the eraser. Actually I used the store brand which is considereably cheaper. It worked great! Good Luck.
Try rubbing alcohol. I've used it to take Sharpie ink off of plastic and glass.
Try aerosol hairspray. Our local "dented and dinged" grocery store marks their prices with sharpies and they have a sign at the registers to use hairspray if you want to remove the price. Worth a try.