Do you give back sentimental gifts?

I had given my most recent ex a white gold necklace with a pendant consisting of our initials and a heart along with our favorite gems. She made it clear that she thinks it best to part ways from anything your exes have ever given you (she went as far as to make me give her a dress suit I was gifted before so she could get rid of it), but she chose to not return the necklace to me. I also can’t see why she didn’t give me the suit back if just a week later she was going to dump me. Im just so confused.