Everything has its opposite. Even crime.
Thus, but not very often in a city as venal as Ankh-Morpork, the Watch is troubled with reports of proffering with intent, or breaking and redecorating. Anti-crime mainly consists of what we consider charitable or "good" acts, but done in a way so as to inflict shame and humiliation on the victim. For example, whitemail consists of threatening to reveal a mobster's secret donations to charity.
A specialised sort of anti-crime is described in I Shall Wear Midnight. Here, the NacMacFeegle reveal a hitherto unsuspected creative streak as they are forced to resort to anti-vandalism. They first restore a complex glass mirror-ball which has been shattered into a million glass shards when inadvertently dropped by a coachman with jumping bones. Then they top this by rebuilding the King's Arms, a pub which they were responsible for destroying during a stand-off with the Watch. Admittedly, they rebuild the pub backwards, necessitatiing a change of name, but do it so well that it arouses the ire of Commander Vimes, who now has nothing except circumstantial evidence on which to arrest them. Here, the humilated party is the Watch.
Professor Hix, the University's licenced Evil Wizard and amateur dramatics player, has perfected a sort of reverse pickpocketing, by which he deftly adds to people's pocket contents by inserting free tickets to Dolly Sisters Players productions, thus condemining the recipient to an evening of truly lacklustre amateur theatre.
There may be a thread leading back from Anticrime, to the first faltering steps into crime made by the Piranha Brothers (Doug and Dinsdale) in the Monty Python's Flying Circus sketch. Being new to crime and not quite having got the hang of protection rackets, the Piranhas would select a victim, and threaten not to beat him up as long as he didn't pay them any money. (After a couple more tries, they got it right, by a process of trial and error.)