There are two episodes in iCarly that feature mixed martial arts (MMA), and those episodes are iFight Shelby Marx and iLook Alike. The writers of the show, in fact, did not use the incorrect term, "Ultimate Fighting," and did indeed call it "mixed martial arts."
In iFight Shelby Marx, Carly and Shelby Marx fight in a cage that is an Octagon, which is a trademark of the Ultimate Fighting Championship (UFC). They fight in the CFC, which is actually the initials of a real MMA organization, the Cage Fighting Championship. Also, they do not use boxing gloves but real MMA gloves.
Other episodes where mixed martial arts was displayed was in iCook where Sam used an armbar on Ricky Flame and briefly in iPsycho when Gibby was fighting Nora using things like takedowns and judo throws.