I soak my dirty buttons in lime or lemon juice (citric acid) diluted with just a bit water for about 20-30 seconds then I start to brush it with a soft bristle toothbrush. I'll brush it a bit..take a look...then dunk it again for about 5-10 seconds and brush until I clean it up. You don't need that much juice. Just prop a bowl up on a diagonal. Put 1 or 2 oz of juice and 1 oz of water in the vessel (enough to submerse the button) and have at it.
Everyone I hunt with does the same. The only risk you run is "burning" the button by exposing it to the citric acid too long. I have never burned a button that way...but I know you can. To burn a button you have to leave it the drink for a long time to do it. That is why I dunk it for a short time and then lightly brush it. When I am done brushing, I'll do a light rinse with water, let it dry, and smear a light coat of petroleum jelly over my button.
Everyone has a different way of doing things!!! Your button might look a little worn to most, but to me it shows promise to me. Under that dirt might be a beauty!! I have seen much dirtier buttons come out looking very close to new.
Best of luck!!
Sneaky6