I looked for a way to remove scratches from my old iPad screen, and all the recommended methods seem to involve using a very, very fine abrasive cream of some sort. I guess the idea is that you buff out the visible scratches with something that makes even finer scratches that you can't see
I never used any of these ideas as they seemed likely to do more damage than they repaired, but you can find them by Googling something like "removing fine scratches from plastic screens".