Only because they represent the time you hurt so badly on the inside that you had to transfer the pain. Otherwise, the person who did it...they're still here, the same as any scar. I mean, an opponent who isn't physical but wants to harm you is still one you've overcome by being HERE and now, right?
At least that's what I want to tell my brother when he's worried about the ones he gave himself.
...That said, if you know someone looking to get rid of scars, I've got a few of my own from...other reasons and I'm okay at hiding them from my Da and Warder.