The Star of David is a symbol of Jewish identity. Over the course of the play, we see that Peter would like to erase his identity and move on with his life. He sees the Star as a source of shame and humiliation. Anne, however, sees it as a symbol of her heritage.... something sacred.
Anne. (She starts to throw hers in, and cannot.) It’s funny, I can’t throw mine away. I don’t know why!
Peter. You can’t throw . . . ? Something they branded you with . . . ? That they made you wear so they could spit on you?!
Anne. I know. I know. But after all, it is the Star of David, isn’t it?