What burned the marble - and is it real marble or a manmade look alike? Real marble is hard to burn, a hot pan is not enough. I have a marble tiled hearth and it has not burned despite getting hot coals on it.
If it's a synthetic, try bleach. There are entire websites devoted to cleaning genuine marble.
The product referred to is "bon ami" (the can is a gold color). I'm not sure where its sold (I think grocery stores carry it (I usually shop at a military instillation)). It is less abrasive than regular scouring powders. I think this is the stuff you are looking for. My grandmother used it on her cook top (the first of the glass top stoves).
They make a certain cleaner for flat top stoves. Very strong, but unabrasive. Probably find it at Wal-Mart. You don't want to ruin the finish, so yes, use a soft cloth.
As others have noted; a mild tootpaste can be tested also, but be sure that you test it in a non conspicuous area first...you don't want change the surface texture...
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