I don't know what will get it out, but you can always get it Rhodium plated to make it look good as new. I usually do this once or twice a year just to protect it. I would also recommend that you don't wear any rings per AORN recommendations.
Try scrubbing it with an old toothbrush and crest toothpaste. Years ago, before we knew mercury was so dangerous, I was rolling some around in my hands and got it all over my brand new engagement ring. My dad told me to try the toothpaste and it worked like a charm. Good luck.