The only way you can remove paint from most any surface is a product called, "Goof Off", which removes latex or water based paint. Or, a regular paint thinnner for oil based paint. BUT either way it will probably dull or change the original wood surface. Id try these by taking a rag , and putting just alittle bit on the rag and rubbing it in a circular motion , ( in an inconspicuous spot), just to see what kind of paint it is, and if it loosens up or dilutes alittle when the product is applied. Its probably latex ( water based) so i would try the Goof Off first. Be patient it may take a bit to gently rub it out. Short of that , i dont know what else would work.

Paint thinner will not remove dried oil based paint. Lacquer will remove dried oil based paint but it may damage the surface.

Sorry ,, I was thinking of wet oil paint saying paint thinner,,lacquer is the right choice.