It looked to me that part of her hair was ripped/blasted off from the fight. I think she came to Sakuya so she didn't have half a head of hair. If you look at the first picture,the left half of her hair (our right) looked ragged and some of it is falling out. She was making excuses as to why she needed a hair cut. In truth, she wants to keep her hair. She might even find great pride in it. Its hard for her to have it ruined.