I've no personal experience with this myself, but I've read where people have used acetone (nail polish remover) to remove paint apps on Joe figures. The idea basically is to dip a Q-tip in acetone, wipe it on the app, and then try to rub the paint off with a fresh rag.
Keep in mind that acetone is a dangerous chemical, both to yourself (work in a very-well ventilated area, keep away from any heat or flames sources), and potentially to the figure (it can "melt" the plastic, which is why you only add a tiny bit and wipe it off immediately.)
As I said, I've never used this myself, but adding "acetone" to your google searches might help you find a couple tutorials on the matter.
Do your research and be careful, you can ruin your Jinx (not to mention your health). Good luck.
Here's one I found on HT for you: