In the US, the default rule is that your home is your castle. In general, nobody, not even the police, can enter your home without your permission. The main exception to this rule is that police do not need your permission if they have a search warrant to search your home. To get a warrant, the police must convince a magistrate that they have good reason (ie, "probable cause"), such as a gps track, to believe they will find evidence of a crime if they search the house.
The police in your hypothetical are in a similar situation to police who are tracking the gps signal from a "bait car/bike/phone/tablet/package." (A bait car is a car/etc that has been fitted with a camera and gps tracker, and left out as bait for thieves.)
As long as the car is in public view, the police do not need a warrant to search it and arrest the person driving it. However, once the bait car is out of public view, where the police can no longer see it, they need a warrant to go in and recover it, even if they can see it on the tracker. (See, for example, the instructions for bait car programs from the Eugene and Reno Police Departments.)
(For phones, which may not be in "plain view" even if the thief is, the police use ring programs to make the phone ring. Hearing a phone respond to a ring program gives them probable cause under the "hearing" version of the "plain view" doctrine.)
Bottom line: In the US, the police need a search warrant. Since search warrants take time and effort, police may be unwilling to get a warrant for something as low valued as a phone.
If the police can't or won't help, there are various options for privately enforcing one's rights. These range from the legal -- knocking on the door and confronting the thief -- to the illegal -- left to your imagination.