First, if components of the parody are protected by copyright then, as much as I hate to say it, you had no right to use the components in your work.That is incorrect. Parody clearly falls under "fair use" in copyright law.
Parody only gets a "fair use" exemption if it is being used to comment upon the copyrighted work being used. A parody of "Les Miserables" using music reminiscent of the show would be protected. A parody of "Cats" using copyrighted music from "Oklahoma!" would not be so protected.
There is an enormous fuzzy area, especially in cases where one is producing works in the style of another work. If one were trying to parody something in "Cats" one could get by with music much closer to that of "Oklahoma!" than if one were trying to write an original musical about rural living. In the former case, even if the primary target of the parody was "Cats", one could argue that making a caricature of "Oklahoma!"'s music (instead of merely reproducing it) also served a legitimate parody purpose for the latter.
I think this case is pretty clear: Registered was in the wrong. Nonetheless, the facts that (1) he ceased distributing the image well before a C&D letter was sent, much less received, and (2) the copyright holder has in fact profited substantially from the infringement, should both severely limit damages.