If they are a danger or damage your property you can get someone to trap them and give them an injection.
They are no different than the mice or the groundhog that was eating my tomatoes and destroying my whole garden. I got a trapper whose job usually involved trapping skunks but this time it was a groundhog.
State and Interstate regulations prohibit transporting the animal to the countryside because they may end up confused and dead on the highway.($10,000 fine)
The cats in your yard are a result of someone’s negligence who released an animal that they were tired of.
An economic liability, and especially a health hazard, should outweigh the consideration for animals that the Torah expects us to show us to animals.
A shelter will probably give then to another home where they’ll outstay their novelty and again be thrown on the street.
I’m certainly not a rav,so if you think there’s a problem, go ahead and ask.
This was just another opinion that most would be afraid to post.