It is impossible to admonish, throw hints at, or guilt trip someone who is behaving rudely on purpose. A cat does not sit on your newspaper because he is confused; he sits there because he knows you are reading and wants attention. Here, Garfield fully understands that he is disrupting Jon's romantic intent, snubbing Liz, and willfully disregarding Jon's forceful hint — refuting it, even, as the man implies that any company would be a third wheel, and the cat deflects the insinuation by pretending it was addressed elsewhere.
Now, as to the Garf's motivation, it is possible that he is asserting his household dominance and demonstrating his primacy to Jon and over Liz. As the devil is a lawyer whose favorite phrase is "well, technically...," Garfield inserts himself into the conversation just in time to assign himself a spot in Jon's vague personal pronoun. If Jon wants the company of One, that should, can, and will only mean Garfield.
On the other paw, this is about the food, and if only two diners will be eating in style tonight, Garfield is determined, assumes, or knows he is taking up one of those reservations.