tortoise shell is exactly that…the shells of tortoises laminated onto a wood substrate. for the most part we stopped doing that a long time ago. it could also be a plastic laminate made to look like tortoise shell. either way refinishing is a no no. if it’s real tortoise shell then it can’t be refinished (there is no finish) some tung oil might restore some luster to it, if it’s a plastic laminate even trying to polish it could ruin it’s face.
Karl F Newman