I'm not sure if its the right thing, but I have had a farrier do it. I had the same problem with a TB years ago. She had a small crack that wouldn't go away. Not enough to affect her performance, just an aesthetics thing.
He didn't trim any away, just cauterized the crack from the bottom with a hot tool and then hot shod her. (he traveled with a forge)
I sold her soon after that so I can't tell you if it did any good