Those lines look like scar lines to me too. I actually try to avoid getting shrooms like that. I don't like cutting my shrooms and rather try to cause them to spawn by careful placement. I know some people are cool with cutting into corals, but I only do that if a coral is sick and I want to start a frag.
Those scar lines rarely go away in my opinion. Unless the ric frags itself off or you cut it again, then those lines are pretty much stuck there.