OK. I just checked the federal trademark database, and, on May 17, 2011, Lippman Law Offices trademarked "Caylee Anthony" and "Justice for Caylee" for use on T-shirts, stickers, underwear, buttons, etc.
These were filed as "intent to use" applications, meaning the Anthonys swore (probably under penalty of perjury lol) that they intended to use these trademarks on the goods identified. But IIRC the Anthonys announced at the same time they filed the trademarks that they had no such intent and just wanted to "stop other people" from using them. IMO if someone else was actually using (not just intending to use) the marks before the Anthonys filed (or actually used them), the other person would likely prevail in a trademark dispute. You can't register a trademark just to stop someone else from using it.
IMO there would also likely be a First Amendment defense if anyone used the marks in a non-profit way to bring attention to the lack of justice for Caylee.