Driven5 said:
It came into your garage to ask for a ride to get warmed up at a local vet or shelter. If it's microchipped, let them retrieve it from there.
That's the solution. Depending on how the laws are written there, it's often illegal to allow your pet to roam in that manner. This means that a cat or dog that is doing so can be humanely trapped and turned over to a shelter.
In my case, there were many dozens of cats in the neighborhood when we moved here about ten years ago. I trapped a few for transport to the county shelter for sterilization and rehoming. That was only a small percentage of the total, but almost all of the rest disappeared. I suspect coyotes.
Edit: I was able to do so because I had an enclosed section of my property where no one could see or hear the process. Also, when I went to the shelter I identified myself as Mr., not doctor.
If this results in a war with your neighbor, it's not worth it.
I don't know how effective that spray is, I have no personal experience with it. A motivated cat is pretty difficult to discourage. However there are things I know will work. If it's outdoors, the motion activated water sprinklers will do the trick, and work great. However, that's not at all possible in freezing temperatures.
for training indoors cats to avoid things like jumping on the counters, there are motion activated compressed air cans (brand name in the photo):
...and plastic mats with imbedded wires (Scatmat),
...which would be my suggestion.
Just don't buy anything other than the trademarked original version of the Scatmat, the copies are unreliable. They come in various shapes and sizes. One or two of the long, narrow ones, depending on the width of the door, would be very effective.
I'd put it down long enough to establish the deterrent effect, and then put it away and replace it with a piece of plastic carpet runner. The cat won't know the difference, and you won't have to worry about running over it with your car.