Garfield often trades in the absence of objects, ideas or feelings to conjure the presence of a joke: food Garfield has stolen, Garfield's failure to respond verbally to Jon, or lack of empathetic response to Jon's problems. Above, the absence of the dog itself seems at first to inadequately justify or explain a sign warning against it. The 1, 2 count of the joke being if the dog is shy, the (sign) reader needn't be wary, and the sign is the only testament to a dog that is so shy it would not otherwise appear. That is, the sign contradicts itself in multiple, self-defeating ways, while serving only to put the dog, who wants to be left alone, front and center in the reader's mind.
A knee-jerk response might be to say the strip would be funnier and achieve the visual sparsity in Garfield that I'm always talking about, if the dog did not appear at all in the final panel, leaving only the empty lawn and sign. This was my own reaction on first read, but the reveal of the dog confirms its existence, and further extends the complex play between language and visual . The already confused sign, which has the appearance of making sense while seeming to achieve opposing goals, finally does protect the dog, in spite of itself. First, the dog is visually concealed by the sign. The most basic level - the physical impossibility of the large dog squeezing itself behind a small sign - doesn't concern us so much as that the signifier ends up physically masking the object signified. Secondly, the language on the sign is so muddled that it cannot be decoded properly; unable to entirely map the territory to which the signifier points, Garfield chooses "SHY" as the key idea over "BEWARE". Despite approaching from the side where the dog is hiding, and seeing the dog, Garfield walks past without a glance, assured not to worry by a sign that would seem to say the opposite. The dumb-tongued intent of the warning ends up functioning to protect the dog's feelings and the passer-by, leaving only the third party in the audience with full comprehension.
The whole episode points to another Garfield truism, that announcing one's own failings and negative traits loud and proud tends to help you get what you want, for better or worse.