The legal issue isn't that it is like a GPS tracker, it is that it is a physical trespass (a fairly well-defined legal concept) for the purpose of establishing information to be used against you by the government.
Now, this is also a feature of the GPS tracker case, but it's not the comparison back to the GPS tracker case that is the main issue, but the same underlying principles that have governed the GPS tracker case and a wide range of others.
They aren't illegally entering the car, they're putting chalk on the outside of it.
Yes, without permission, dumping on someone's property is a trespass.
> So to would leaving a hand print on someone's car if you happened to touch it.
It is a trespass, yes. Probably not on its own an actionable one (or at least not one worth civil action) because of the lack of harm, but whether a trespass would be actionable or worth action as tort is irrelevant in the case where you are looking at a Fourth Amendment violation where any trespass by givernment for gathering information to be used against a person (as a violation of legal property rights) is, ipso facto, a violation of an expectation of privacy, triggering the requirements associated with a search.
I'm assuming the marks are put on the tread of the tire and if that's the case then it only reasonable violates your privacy for a short duration. This is akin to being seeing in the local strip club parking lot however far less scandalous.
The fact of the matter is that all cars have a unique identifier clearly visible on at least one outward facing surface. It can just as easily be used by LOE to determine how long you've been parked in a spot with a simple app that snaps a photo and logs GPS coordinates.
The differences being that chalk is temporary and can communicate to interested parties that you've parked recently in local vecinity, where as a license plate requires instance observation to track your movements.