Hello could you possibly post a photograph to better see your situation and area of stain damage? Having a visual might be best guidance to a help find the best suggestions or potential solution to best know what you are dealing with.
Marble is basically compressed limestone. Any acidic cleaners will etch, dull and stain the surface, including vinegar, citrus cleaners, and lime/calcium cleaners.
If you are trying to remove an old stain, create a dense paste of more baking soda and less water. Then place the paste over the stain, allowing it to function for a few minutes. After that wipe off the baking soda paste. If it is needed you can repeat the procedure until the stain vanishes.
If the stain is persistent and is still there you can try removing it with ammonia solution. Make the area of the stain damp with 10% ammonia, diluted in water. Ammonia is knows as a base solution, so it is suitable for removing stains from marble.
The final stage of the stain removal us rinsing. Rinse the solution from your marble well to eliminate any residue, left from the cleaning ingredients on it.
I advise to use gloves when removing the stain with ammonia. They will protect your hands. Ventilate the room, in which you use ammonia for removing stains, because it is toxic.
its very hard to remove stains from marble almost impossible. Contact a company that sells marble and they may have some new technology.
You could try bleach on a sponge
Baking soda and rub lightly with a microfiber cloth.What ever you do, DO NOT USE VINEGAR it will etch the marble. You could also try tooth paste.