The narrator tells us that, after the dog incident, not much happens in Iping until the club festival (which is around the Christian holiday of Whit Monday). Instead, the village settles into something of a routine.
This is the routine: when Mrs. Hall complains about his messes, the stranger tells her to bill him extra, which works fine until April, when he starts to run out of money.
No one in Iping really likes the stranger and everyone has a theory about why he's so weird. (How strange is he? He doesn't go to church on Sundays and he goes for walks at night. Clearly there's something wrong with this guy. Where are the police when you need them?)
Some people think he's a criminal or an anarchist or a lunatic or simply a freak who could make a fortune charging people at county fairs to check him out.
Whatever his deal is, everyone seems to agree that the stranger is too irritable for a village, "though [his irritability] might have been comprehensible to an urban brain-worker" (4.8).
One villager who does want to talk to him is the town doctor, Cuss. On Whit Sunday, Cuss goes to talk to the stranger – partly because he's curious, partly because he's jealous of all his bottles. After the talk (which we don't see), Cuss runs out to see Bunting, the vicar.
(In case it's an unfamiliar term, a "vicar" is a parish priest in the Anglican Church. So, he's kind of a big deal in the town.)
Cuss wanted gossip, but this is apparently what happened instead: while the stranger was telling him a story about why his research was taking so long (a scientific formula got burned in a fireplace), the stranger revealed that his sleeve was empty. Then he seemed to use an invisible hand to tweak Cuss' nose. To be clear, if you're trying to hide the fact that you're invisible, tweaking people's noses with your invisible hand is not a good strategy.