You will need to "wet sand" the marble surface with a very fine grit wet/dry sandpaper. (like used for automotive paint finishing, and can be found at auto parts stores and "some" hardware stores.)
Start out with 1000 grit and work your way up to finer grit paper until you achieve a nice smooth finish. The finer the grit, the smoother the finish. be sure to keep it wet while sanding.
Then, depending on the level of shine you want, you can then buff the surface with a polishing compound made for limestone, marble, and other soft stone work.
Marble is a limestone based substance, so anything even mildly acidic will mar the surface. I was the soaking in that solution that caused the problem.
You might want to invest in a "dremel" rotary tool and use nothing but a polishing wheel and polishing compound.
Do not use anything abrasive (like sandpaper of ANY grit) with the dremel tool.
To get into all the engravings, you may need to buy several different sized and shaped polishing tips.
Dremel tools and tips can be found at Lowes or Home depot.
Here are a few links/pictures of dremel tools and polishing tips.
http://www.dremel.com/en-us/tools/Pages/CategoryProducts.aspx?catid=13&catname=Rotary+Tools
The polishing wheels and points are made of cloth and felt.
http://www.contractorsdirect.com/Tile-Tools/Polishing-Pads-Buffing-Compounds/Dia-Glo-Diamond-Buffing-Compound;jsessionid=0a010c641f43c247a75e1fda4019b176d6390ed633af.e3eSc3mSaxuPe34Pa38Ta38Lbhr0
You should also be able to find marble polishing compound at your nearest stone counter top supply store.
plumber and HVAC tech
16 years experience in Home Improvements specializing in HVAC and plumbing. Self employed for 6 year