Might be* a reference to the color of the tounge. 'Venetian Red' is a known and used color. Why that's funny I couldn't tell yah, but digging on Webster, this was what made the most sense.
Yeah, that's what I thought as well. I've seen a bunch of these old Garfield comics over the last few months, and I have to say most of them were pretty awful. Was Garfield really that bad? Growing up I only remember the cartoon and even that I couldn't tell you a single thing that actually happened at this point. I hope it was better, otherwise I have no idea how Garfield still exists today.