Perhaps this will take care of it: https://www.hunker.com/12151486/how-to-remove-vinegar-stains-from-marble-surfaces-like-countertops-and-floors
The vinegar has chemically etched the marble. Citrus, tomato & wine will also do this.
I would wash it w/ baking soda water, rinse & buff dry. Then I would apply 3 separate coats of non-yellowing marble sealer, in a buffing motion.
If you need to hand re-color the marble etching with artists markers, then do that first or after the first coat.
For my marble countertop, I make a paste of baking soda and water, then let it sit on the spot for a while. Bad spots need 2-3 hours. After you clean the mess and the marks are gone, seal the marble with stone sealer. It's just wipe on- wipe off.