How can I repair a burn mark on fake marble?

It’s melted the plastic and there’s a few things that might work:

Polish out the burn, if it is shallow, with an abrasive, like comet or Ajax and a wet sponge.

If it’s deeper, consider using wet-dry sand paper, 500 grit and then 1000 grit and lots of water.

Use circular motions & a rubber sandpaper block with the concealed teeth (auto parts store).

Hi Kathleen. Oops! Cultured marble is easier to repair since there's no repairing true marble. First scrape out all the dark stains. Then use plaster of paris to fill in the gap. Using acrylic paints, replicate the surrounding area. Use a sealer on top. If it's a very small area, clear nail polish will do. Good luck.

you can do the above then once clean if there is a divot, use Super glue to fill the hole. Then when dry use a flat razor at a 90 degree angle and make it flat. Works on granite too.

Don't use plaster to fill in use Bondo it's waterproof, plaster us not. Shave flat with a razor blade paint to match the top. Seal with poly.

it might be helpful for you.. https://www.youtube.com/watch?v=YrgmCP7BHDI