I posted this on the Facebook group a couple of years ago, but the topic keeps coming up, so I am making this page to have as a convenient link.
Normally I dislike altering or customizing my Lego bricks, but sometimes it is useful to be able to remove the printing from a piece. I had a lot of Chima heads printed with two faces that I wanted to be able to use with normal hats.
I looked around online and saw a near-universal consensus that Brasso is the best way to remove paint from Lego without harming the piece. Back in the early 2000's people tried lots of things and shared tips, and concluded that Brasso worked best.
The smallest size is all you need, just put a pea-sized blob on a cloth and scrub the painted area. I tried it, and it worked very well. Each face took about a minute. Four or five strokes would remove the section of the face touching the cloth. Repeat a few times moving round the circle and the job is done. There was no damage to the piece at all; it looked like it came from the factory with only one face.
Some other notes:
The printing on torsos is a lot thicker and harder to remove. Brasso took far too long. For those, people recommend scraping off the paint with a new 'sword of exact zero'. But when I have a torso with inappropriate printing, I just put a suit of armor over it.
Do not use Acetone; it will melt the bricks. Acetone dissolves ABS plastic. People use it to weld pieces together, or completely melt them to make Lego paint to apply to other bricks. However, if you have used a mechanical scraping process that damages the bricks, you might be able to use a little bit of acetone to melt it back to a smooth finish.