If the paint is water-based acrylic/latex you can try this method, which is used to remove paint from glass:
1. Get some cloth rags, a set of kitchen tongs, and a pot of water.
2. Bring the water to a boil on your stove, and toss a rag in.
3. Remove pot from the heat and take the rag with the tongs and place it on the area you wish to remove the paint from and allow it to heat the area up. Don't leave it on the plastic too long though which might cause the plastic to warp or deform. Basically, you just want to break the bond of the paint to the surface it's applied to.
4. Use the clean kitchen tongs to hold the hot rag and scrub the paint.
The heat will act as a release for the paint, and you can continue to scrub at the paint as it cools.
Not sure that this method would work on solvent-based paints ... due to the action of the solvents on the plastic when the paint was originally applied.
As always YMMV, end-user assumes all risk, nothing in this post should be considered medical or legal advice, consult with a qualified, competent doctor or attorney.