This would be the second call from the attorney, the first being when Dr. Mat and Company were first introduced and he was speaking ill of the S-Team.
Tribbles, of course, are from Star Trek, and this references the fan-favorite episode with my favorite non-cast character of Harcourt Fenton Mudd (HAVE YOU BEEN DRINKING AGAIN???) and the cute, Klingon-hating Tribbles. Gremlins are from the eponymous movie, and there were specific rules you had to follow (that didn’t make a whole lot of sense except for the purposes of plot advancement) about not getting them wet or feeding them after midnight.
The “Say it with me” line is a reference to Mystery Men, when Mr. Furious, the Shoveler, and the Blue Rajah first meet the weapons designer, Heller. (“My name is Heller. Say it with me…Heller.”)