Sand it down:
You will have to sand it down in steps. The first step will remove the staining the rest are to bring it back up to a polish.
60 grit120 grit220 grit400 grit600 grit
Apply a silicone sealer (mineral spirit based- not water) to the stone. Follow the instructions on the product label.
Then I would advise you to maintain it with a high quality marble wax about 1 time per year.
Don't use muratic acid (or any other acid) on it anymore.
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