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I would try a solvent like mineral spirits, rubbing alcohol or denatured alcohol first. There is also acetone and lacquer thinner but you have to be real careful applying these two, the solvents on these two are really strong/hot and they may just melt the finish/gel coat like butter, I do not recommend them.
Also you may try an automotive rubbing compound follow by a polishing compound and this should take care of of the scuff marks. Before you apply these compounds make sure you wipe clean the drum with denatured alcohol, rubbing alcohol or mineral spirits. I hope this helps.
White scuff marks are often due to scuffing of the surface, which turns opaque white, rather than some foreign material actually getting on the surface. Agree with RB that rubbing it out with rubbing compound may be your best bet. Would try it on some unnoticeable spot first, maybe take off the bottom band and test a small spot of paint underneath where the band goes. Also agree with being VERY careful with the organic solvents and sticking to mild solvents like water and alcohol just to clean grit off, then try the rubbing compound.
Ritmo is right. Forget about the thinners. You'll ruin the finish then have to refinish it. Get the white rubbing compound at the hardware or auto parts store. It's really easy to use. Just follow the instructions on the container. This should work very well. Good luck.