I'm not trying to erase anything; I'm more encouraging these players to make their background fit the game world better because in the end, the game is just collaborative story-telling and you're not the only writer. Just as it's easy to fix the problem with magic, you could equally make it unfixable with magic too.

You've clearly internally defined magical healing in a way that makes it somehow know in which ways a body deviates from the population median, even if it has never adhered to said median, without thinking about how it might know how to do that.

Magic is literally capable of anything. It can grant wishes. It can raise the dead. It can cure disease. It can also cause death. Cause disease. Permanently maim and disfigure. It doesn't need to know anything; the person performing the magic makes that determination. That's part of what makes it magic.