I don't know if it's damaged or not, but I doubt that's carbon. That's most likely cupric oxide which is a black oxide of copper and is often used as a protective or decorative finish. It develops from chemical reaction with water or with alkaline chemicals.
The next question is, how deep does it go? I would take a pocket knife and do a little scraping to see how far down the brass is. Probably not too far. I've had it on corroded cases and they didn't lose more than a fraction of a thousandth when I took it off.
The way I removed it was with a citric acid solution in an ultrasonic cleaner. The photo below shows the black oxide surrounding green oxide on brass that was in a baggie that got flooded on a concrete floor. The water and concrete provided some alkalinity which promotes the black oxide formation. The nice thing about citric acid is it doesn't attack the underlying brass, but rather tends to passivate it. Citric acid treatment is a common method of treating brass before putting it into long-term storage, as it is then protected from coarse corrosion. You can leave it on a shelf indefinitely with no further treatment or polishing. A slight darkening of the yellow color is all that happens over time. However, after treatment you may see some pink where the oxide was. That's copper from which the zinc in the brass alloy has oxidized out when the stain was forming. That polishes right back to brass color and is the only reason I can think of for polishing afterward. Polishing removes the passivity and leaves the brass more vulnerable to corrosion (no more than any other polished brass) again. The citric acid treated surface is the best for long-term storage.
Since it is fall, you can probably get citric acid where canning supplies are sold. Ball brand has it. Walmart used to have it in fall. But if you start really liking citric acid cleaning,
I buy it from this place postage paid. He sells all quantities you might reasonably be interested in, but it does cost a lot less per pound as the quantity gets larger. If you can interest friends in a group buy, you’ll save the most.
For wet tumbling and the like, a tablespoon of citric acid powder in a gallon of water is enough. However, for black oxide, use a solution that is 5% by weight. That's the old Frankford Arsenal brass cleaning formula from before the military started leaving the annealing stain and oxides on brass. They started that practice sometime in the 1920's, so the formula is probably from World War One or thereabouts, but it still works fine. Just put 7 ounces of citric acid in a gallon jug, fill it 2/3 of the way and cap it and shake it until the powder dissolves, then fill with water the rest of the way to make a gallon. With the citric acid I got from Duda, 7 ounces turns out to be about one measuring cup full. That’s close enough if you don’t want to weight it. Heating it to about 140°F speeds everything up considerably, but is not required if you have time to wait for it to work.
On the leftmost case, below, you can make out some pretty dark black to the left of the outer verde gris ring at the bottom and on the inside of the ring around the center green area. On the other cases it just seems to be mixed in with the verde gris. The verde gris vanished in about 15 seconds in the hot solution, and the black took longer, but I don't recall timing it. Carbon and primer pockets took longest to clean. The oxide was long gone by the time it was done with primer pockets.
