Actually, it's option three: John feeds Elly a straight line. The subject of the alleged joke is Elly's aggravating refusal to admit that trying to talk Farley out of a bad habit is futile because, despite what she wants to believe, he isn't a human being in a dog costume.
Panel 1: We start off with New-Ruin Elly in the garden looking gobsmacked because Farley is barking at something on the other side of a fence they don't usually have.
Panel 2: Instead of seeing what it is that he's barking at, Elly yells at him.
Panel 3: Farley starts barking at the unknown and unknowable presence that agitates him again.
Panel 4: Elly puts her hands on his muzzle and says "Stop barking, no barking, NO!"
[ETA: At this point, you almost wish that Farley would up and nip Elly for being a jerk.]
Panel 5: He resumes barking at whatever it is that's bothering him.
Panel 6: Elly yells "No barking! QUIET! STOP! NO BARKING! NO!!"
Panel 7: Having seen him resume barking, it suddenly occurs to me that there must be something or someone on the other side of the fence that Elly needs to find out about. Instead, her face gets all scrunched up with rage.
Psnel 8: She then yells "That's enough! Stop it! No Barking! Too much noise! No! No! NO!!"
Panel 9: Farley, who didn't understand a word Elly was yelling, gives her a confused doggie smile as he wags his tail and wonders what the loud lady wants.
Panel 10: John asks Elly how she spent her afternoon; she tells him she spent it barking at the dog.
Summary: Dogs bark at passers-by because that's what their instinct makes them do; if we have the patience and brains Elly so clearly lacks, we can train them out of it. We can also find out what the things are that set our pets off so as to minimize the risk; too bad Elly is too stupid to look over the fence and see what's got him so agitated.