What do you mean it moves around? Are you using a liquid, and when it dries the spots reappear, or is it a stubborn speck that you can't remove from the screen, and you just keep pushing it around?
It's a removable screen, right? Take it out, if you haven't already, and beyond a camel's hair rush, I'd say a lens cleaning solvent might be ok, but I can't say with absolute certainty.
If nothing works, you could get a replacement screen or live with it, as it won't have any affect on picture quality. Good luck!