Garfield loves jokes that point out our conditioning to rules, control systems, and society's behavior restrictive constructs. By extension, Garfield questions and draws attention to ideological apparatuses, though the conclusions drawn are largely more observational and defeatist than progressive. As today, this is usually manifest as i) the application of a familiar rule system to a situation in which it cannot logically restrict, or ii) the continued cooperation with outmoded rule systems well past the point of usefulness, outside logic, or the original intention.
This is best demonstrated, as above, in individual strips and jokes, but is reflected to a degree in the general plot/situation and regular behavior of characters. Garfield continues nominally behaving like a cat, despite opposable thumbs. Jon and Garfield watch endless amounts of television less out of enjoyment than cultural obligation. Odie frequently puts himself in position at the edge of the table, waiting to be kicked, because he has internalized his role in the stock situation.
The Beware of Dog strip above relies first on our recognition of the omnipresent deli numbered waiting system, and the absurdity of a dog having access to and understanding of this system, and the mechanical ability to install it. That is fine and good, but the real mystery and contradictions are dense and endless. Why would anyone wait in line to be bitten? Don't we sometimes wait in longer lines for equally miserable, arbitrary tasks? Doesn't the acceptance of the waiting line by participants negate the purpose and message of the "Beware" sign? Why do people choose to obey one sign over the other? Do we simply try to compute every fresh directive, even when it contradicts prior knowledge? Why does Garfield take a number and take his place in line? His weary sideways glare tells us that he has the ability to see through the inanity of the situation. The Garfield conclusion tends to be that self-awareness is not a free ticket self-improvement. Knowing where you are does not set you free.