Lawyers for Monaco “royalty” Pierre Casiraghi and his posh pals Vladimir Restoin Roitfeld and Diego Marroquin are desperately trying to clean up their images, which were bruised by the “Battle Royale” — and have fired off a sternly worded letter demanding that negative things previously said about them must be retracted. The trio, along with Stavros Niarchos, were involved in an infamous brawl with businessman Adam Hock at Meatpacking club Double Seven in February. A letter from the “prince” and his pals’ lawyer Robert Dembia to Hock’s attorneys Joe Tacopina and Sal Strazzullo, seen by Page Six, demands: “I am writing to demand that each of you issue retractions of all of your false statements . . . on your letterhead, in writing . . . My purpose is to deliver your retractions to the appropriate news outlets in an attempt to repair the damage you have done to the reputations of Mr. Roitfeld, Mr. Casiraghi and Mr. Marroquin.” The letter goes on to issue a wish list of statements they say must be retracted, including one made by Hock, “They expected to be treated like the royalty they are. They didn’t get what they wanted, and it pissed them off.” It also itemizes Strazzullo’s offending comments such as, “They threw the first punch,” and Tacopina’s quotes including, “They’re international bar brawlers. Paris, Belize, the US . . . These four are a bunch of self-entitled punks who don’t have anything better to do than spend their parents’ money.” And Tacopina’s comments about Princess Grace’s grandson Casiraghi, who had claimed his injuries forced him to take a month off work, “This poor kid who doesn’t work, couldn’t work for 30 days . . . I think what that means is that he couldn’t go to the club for a month.” Strazzullo said, “This lawyer has no basis to ask us to retract anything. If he wants to get a lesson in the law I will gladly give it to him.” Tacopina told us, “We stand by everything we said.” Hock is fighting misdemeanor assault charges and will be back in court next month.