Biting his lip, presumably that he does not laugh or say (read: "think) a rude rebuttal. Jon obviously understands the signal anyway, and is hurt and angered, so if this were an attempt by Garfield to save Jon's feelings, it's backfired. In the instant karmic/insano-cosmic retribution of the Garfield-verse, your internal negative thoughts and judgment are going to shine through half-hearted attempts to be nice anyway, so why bother?
Or does Garfield really try to hold his tongue? Normally, snappy answers to Jon's stupid questions are Garfield's stock-in-trade, so why would he censor himself today? The cat is unable to speak, and in strip production considerations, having him laugh at Jon out loud was a gag used last week, but the requirements of the scene are that Jon lose his cool because he understands Garfield's thought. Garfield is able to convey skepticism and condescension through expressions normally signifying an attempt not to communicate, here the lip-biting ironically reveals more than Garfield could express without it (i.e. - he can't talk). And this, we may suspect, and surely Jon does as well, is a calculated move to have it both ways: Garfield gets to look like he didn't want to burst Jon's bubble, and gets to insult him by implication.
Bonus Funny: Man plagued by self-doubt even after new girlfriend gives him first confirmation of basic human worth in years, takes this problem to the source of most of his self-esteem issues.