Here is the tricky part: City law dictates that any captured raccoon must be killed in a humane fashion, because raccoons are known to carry rabies. But many trappers, as well as homeowners who do the job themselves, say they transport raccoons to parks or wilderness areas and set them free instead, because they don’t have the heart to do what is legally required.

Indeed, many of the trappers who were interviewed expressed misgivings about exterminating healthy raccoons — displaying an empathy they did not feel for, say, roaches or bedbugs.

“It used to be a little different,” said the man who took the raccoon from Ms. Hooker’s yard, and who asked to be identified only as Don because he releases raccoons rather than killing them. “I am in this for three generations. I go back to the time of the drowning barrel. Guys who trapped animals used to have a 55-gallon drum, and you’d just upend the cage and dump it into the barrel.”

“Now,” he continued, “everybody is just releasing them. They’re letting them go in any quiet place.”

Image Encounters between raccoons and people have increased. According to official data, New York's 311 help line received 1,581 inquiries about raccoon control in 2015 as of mid-December.

The problem, experts say, is that from there, the animals tend to wander into the nearest neighborhood. People see wooded areas as the animals’ natural habitat, where they belong. But these are city raccoons that tend to make a U-turn for civilization when dropped off in nature, said Stanley D. Gehrt, a wildlife ecologist at Ohio State University who has studied urban raccoons for two decades. “When you take them and drop them off in a natural environment, they’re going to look for buildings,” he said. “It’s what they’re used to.”

And so, it appears, the spread of raccoons is being aided by the very people employed to combat it.

A special license from the New York State Department of Environmental Conservation is required to remove “nuisance wildlife” such as raccoons. Officials at the department, which has licensed around 100 trappers in the city, said local health departments have jurisdiction over raccoons and other rabies-carrying species. A spokesman for the city’s health department said trappers were not permitted to release raccoons caught on a homeowner’s property elsewhere, “and if they are doing it, they’re doing it illegally.”