Add several drops of acetone-containing nail polish remover to a microfiber or lint-free cloth. Wipe the dried nail polish off the natural stone in a gentle, circular motion.
Pour 2 tablespoons of 3-percent hydrogen peroxide in a small bucket if the nail polish remover didn't completely remove the nail polish. Add 1 cup of all-purpose flour to the peroxide and mix with a spoon.
Add cool water to the paste 1 teaspoon at a time -- mixing after each teaspoon added -- until the paste has the constancy of peanut butter.
Scoop a dollop of the paste out of the bucket with a plastic spatula and spread over the remaining polish. Apply the paste in an even, thick layer that extends a few inches out from the nail polish.
Cover the paste with plastic wrap and tape the edges down. Leave the paste on the tumbled marble for up to 48 hours until dry.
Remove the paste off the marble with a sponge damp with water. Buff dry with a lint-free towel.