Well, challenge accepted.
A crew "revised" the very first piece Team Banksy created this month, a boy reaching for an aerosol can on a sign that reads: "Graffiti is a crime." The sign was swapped out for one that said, "Street Art is a Crime."
In other cases, rivals have simply scrawled over his stuff.
On Monday, while a small crowd was gathered in the Brooklyn neighborhood of Red Hook, a man "ragged" a painting of a red balloon heart covered in Band-Aids and added his own tag, Omar, the blog Animal NY reported.
Later, below Omar's signature, someone added "is a jealous little girl."
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Elsewhere, when Banksy or someone working for him added the stenciled words "The Musical" to some unremarkable Brooklyn graffiti—giving it a "Broadway makeover"—cover-up artists either painted over or erased it.
A silhouette of a dog relieving itself on a hydrant now has some additions, including a misspelled jab at the highly collectible artist, whose works have sold for more than $1 million.
Some dogs have let loose on it, too. And so far, not a word of complaint from Banksy, whose real identity is a secret.
Banksy is the subject of the feature film "Exit Through the Gift Shop," which was nominated for an Academy Award in the documentary category in 2011. Earlier this year, he was caught in the middle of the debate over who owns street art when a third party removed a section of a Banksy wall and eventually put it up for bid at the Fine Art Auctions Miami.
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Councilman Peter Vallone Jr., perhaps the city's most ardent anti-graffiti activist, sounded bemused that the famed graffitist was under attack.
"This guy's a vandal, but a talented one," he said. "This is what the graffiti world is all about. Guys like Banksy are the exception. It's full of bombers and taggers who are no-talents and are just bent on getting notoriety for themselves."
While property owners in the know may be thrilled to learn their building has gotten the Banksy treatment, Vallone noted that he is still breaking the law.
"If he's caught, he should be punished the same way anyone is punished," he said.
In the meantime, New Yorkers are treating the "residency"—which includes a YouTube takeoff on Syrian rebel videos and a souped-up delivery truck with a trompe l'oeil paradise inside—as a sort of scavenger hunt.
Fans check Banksy's website each day for a photo of his newest work, accompanied by the vaguest of geographical descriptions, and then try to find and Instagram it before it's ruined.
In an email interview with the Village Voice newspaper, Banksy dismissed speculation that he might be the one doing the defacing.
"I used to think other graffiti writers hated me because I used stencils, but they just hate me," he said.
On Tuesday afternoon, the Red Hook site drew students from St. Francis College who were on a field trip for a cultural criminology class. They discussed the difference between Banksy and Omar, and agreed the former had more of a claim to the wall space.
"I would say his is art," student Manpreet Kaur said of the broken-heart balloon.
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Neelon noted that battles in the graffiti world are not uncommon, and Banksy may be the biggest target—especially for those who find the frenzy surrounding him ludicrous.
"There are some people who manage to retain the respect of various other graffiti artists and some people who don't," he said.
Ragging—as defacing someone work is called—has only brought more publicity to Banksy, who theoretically has the resources to make his art someplace harder to reach, Neelon said.
"And, of course, he's taking it to New York, where he doesn't stand a chance," Neelon said.
—CNBC's Amy Langfield contributed to this report. Follow her on Twitter, @AmyLangfield.