Here's what I interpreted to have happened with the tracking beacons:
At the beginning, there's two tracking beacons. Let's call them A & B. A is on Mike's temporary car (for potential Hector assassination), B is on Mike's primary car (the black one parked outside his house).
A is left with the car at the junkyard - which makes sense, as Mike would be spooked after the "don't" message and would want to get rid of the vehicle.
After returning home, Mike takes B into his house for analysis, primarily to get the serial #. Once he gets this information, he leaves B at work while he goes out to buy a new beacon using the serial number, which we'll call C. C also includes the actual tracking unit that can show where its corresponding tracking beacon is.
Mike tests the functionality of C, seeing functions like distance & low power indicators. Finally, Mike drains the battery of B by hooking up a radio to it, so that whoever's monitoring B will get the low power message.
Mike places C in his car, and discards B, and waits for someone to come by to replace B.
Side note - replacing the beacon unit here makes sense, as the person tracking likely has multiple tracking systems (they used 2 on Mike with A & B). Replacing a battery on site would be noisy and time-consuming - better to replace with another beacon, take the original back for a new battery, and re-deploy it elsewhere.
Anyways, back to the end of the episode - some unknown person shows up with the intention of replacing B. Instead, they grab Mike's beacon C and leave with it - giving Mike what he needs to follow them. From the mystery person's perspective, B has been replaced with a new beacon, D, and Mike leaves D at home while he drives off into S03E02.