Not sure I understand. Looking at the legal definition of "parody," what creative work of Peck's is being parodied? Does the law allow anyone to say anything about another person if they just say "this is parody?"

From Cornell Law School:

parody

A parody takes a piece of creative work–such as art, literature, or film–and imitates it in an exaggerated, comedic fashion. Parody often serves as a criticism or commentary on the original work, the artist who created it, or something otherwise connected to the work. In the United States, parody is protected by the First Amendment as a form of expression. However, since parodies rely heavily on the original work, parodists rely on the fair use exception to combat claims of copyright infringement. The fair use exception is governed by the factors enumerated in section 107 of the Copyright Act: (1) the purpose and character of the use; (2) the nature of the original work; (3) the amount and substantiality of the original work used; and (4) the effect on the market value of the original work. Generally, courts are more likely to find that a parody qualifies as fair use if its purpose is to serve as a social commentary and not for purely commercial gain.