Doing this right now and have done many as we in the Northwest deal with a lot of moisture. You can either 1st have the chrome stripped at a plating shop where the chrome is just chemically taken off. Then you either start sanding by hand or use somekind of hand held grinder or moto tool. You will then grind all the metal to get the pits outs which are usually pretty deep. Sand with either 80-100 grit paper till smooth, going down in paper till you get to about 600. Polish or buff until smooth and shines.
Now the other way is just to hand this to the plating company and say fix it which will go through the same steps except they will fill with copper and sand and polish. They will repeat these steps until all is filled and they can then put on the final plating which is going to be copper, then nickel, or chrome whichever you want.
Most shops will tell you that it is not worth their time or your money if the pieces are like yours. We have no choices on some of the stuff for pumps.
You can do this your self and then just give it to the plater after you polish and they can put the final platting on it for a much cheaper price, you did all the work.