My other hobby is woodworking, I'm pretty familiar with finishes, etc.
Mineral spirits thins oil based paints and you can use it to remove grease, still soft tree sap, a few other similar substances-- that's it. Will not do a thing to dried, cured, and well adhered paint. What you can do totally depends on the product they used. Certain solvents take off certain paints, which one works depends on the type of paint. In general ascending order of strength are: rubbing alcohol, lacquer thinner, (these two will take off most latex/acrylic/water based paints) and acetone (will take off the former and some oil and solvent based paints). There's also an air freshener called Citrus Magic, don't know if you've seen it, some Walmarts have it, but the orange oil version can remove some paints-- (also kill bugs, dull some plastics, remove some adhesives, clean a lot of stuff, etc.). Most of the above shouldn't hurt the original finish.
After that you're into paint remover products. One I'm familiar with, a thin liquid you can use with a rag (not one of the thick ones you paint on and leave) is called Kutzit. Not 100% certain whether it will affect the original finish.