For me it's definitely taking them out.
2) A person working with me emailed me today and I noticed that they're now using an insulting nickname for me in their contact list (i.e. "insulting name < email >"). I know that they have an equally insulting nickname for our supervisor and are probably sending emails to her in the same manner. Should I inform her that I noticed, it hurt my feelings, and that it's not a good idea to do so, or should I just let the bitch burn?