It is a shame that someone ruined what was probably a nice coin, once upon a time.
If it belonged to me, I would remove it from its holder, then examine it carefully, using several different types of lighting, and different powers of magnification, and try to learn as much as possible about why it was given a no-grade. I would then carry it around as a pocket piece for a year or more, and see if I could give it enough good, honest wear to bring the grade down to at least XF, or possibly high VF. That should be enough wear to remove any damage done by the cleaning. After that, I would store it away for a few years to see if it would get some natural toning. (No Taco Bell napkins or anything else to accelerate color, thank you.) I probably would not send it back in for grading, because that is not my thing, but I bet it would straight grade after that.
If anyone thinks this might be dishonest, let me point out that what I described is exactly what has happened to billions of coins that were pulled from circulation and saved, and are now in collections all over the world.