Was just revisiting this topic because I'm working on a custom atm & had some printing i needed to remove.
I've used the rough end of an eraser method that's mentioned here before & found it hard going + the dull finish afterwards (though I have a way around that).
Thought i'd try something tonight based on some of the other stuff people have talked about.. Rubbing alcohol (regular, not denatured) PLUS magic eraser.
I wanted to remove the printing on the chest of 7176 (My Life lady with dalmation). I put rubbing alcohol on a piece of folded up kitchen roll & wiped it over the area I wanted to remove, then went over it right away with the magic eraser, kept on doing that (wipe, eraser..) & the printing came off SO much easier.
I thought I might end up with a dull finish at the end, but no, it doesn't look any less shiny than the back of her torso (which i did nothing to). If it had I would have tried some fine Novus polish (polish for plastic, great stuff) but it totally wasn't necessary.
Feeling pretty jazzed right now. I'll try & do some more another day & take photos before & after (I have a pretty busy schedule with hospital stuff over the next few days, but will hopefully fin the time & energy over the weekend).

ETA.. tried another with a larger & darker print (the b&w no1 racing car guy that comes free with orders) & that came off really easily & quickly too (with this one it helped & made the removal go faster when I put some of the rubbing alcohol on the sponge itself).