It would be a high-tech remake of an old Low-tech phone number logger...
Back in the old days when phones all had rotary dials they used to capture the numbers that were dialed from a suspects phone by picking up the small sparks that were generated by the make/break of the switch in the rotary dial...you could pick this up from a fair distance on a sensitive radio receiver... they had a small device that worked like a tape recorder with a loop tape in it... after a set of spikes was received they would pull out the loop and replace it with another... later someone would slow down the loop on playback and simply count the static pops and thus discern the numbers that had been dialed..I doubt that this required any warrant...
The modern version of this could be a small thin wafer that goes into the connector of the keyboard... just look at the end of the cable from your keyboard and you will see 6 pins sticking out.... all that is required for a key logger is available at these 6 pins. There is a source of power, the data from the keyboard and a workable conductor to act as antenna. The wafer would be very thin and have adhesive on it's back side. It would be pushed into the connector and adher to the back and become virtually invisible... it would not continuously radiate RF ..but rather send it's data as a series of short rf data bursts that are not that far removed from the old rotary dial pulses from the old dial phones... these signals would not be detectable using simple bug-sniffers like the sort sold to the masses at so called 'spy outlets'. The signals generated by a set up like this could be picked up and recorded by a battery powered receiver/recorder left nearby the targets computer... a car parked outside a house would be a good place to put such a device. Once in a while someone could come by and get the data from the recorder. But there is no way that this sort of system could somehow magically only capture the data from a password entry...so they would be picking up all keystrokes... and it looks like that was a no-no in this case.
These 'wafers' should be very brittle so if messed with they would simply crumble apart leaving nothing functional behind...just what would look like crumbled black plastic bits.