To elaborate: Coop wanted to stop his feud with Kat in honor of the holiday (And also to remain on Santa's Nice List). Unfortunately, Kat wasn't interested in playing nice, and the only thing that kept him from wailing on Coop was his total preoccupation with being homesick. Kat spent much of the episode pining over a hologram of his family and trying to get back to his home planet of Kat Nebula. Coop discovers what's upsetting Kat, and eventually comes to sympathize. So on Christmas morning, Millie delivers a present from Coop to Kat: A photograph of Burt, Coop, Millie and Kat. He assured Kat that he was part of the family, even if they didn't get along now and then.
Dr. K helping Kat and co. get back to Earth, and giving Kat a Big Damn Kiss when he has to leave. Doubles as a Tear Jerker