If the "stray" signal really is on K-band, you actually *want* the radar detector to pick it up. The fact that some motion sensors (be it store security motion sensors or grocery store door openers, etc) actually are on the exact same frequency as police radar makes it difficult for a radar detector to tell the difference.
I assume you know about the two city modes - press in and hold the volume control puts it in the first city mode (display changes from the capital A to something like an L with the upper half missing; the bottom segment and the left lower segment are lit) which will try to figure out which alerts are a threat, and only sound a full-volume audible alert if it thinks any are real (and otherwise sounds only a muted audible alert but still show the count and strength of radar sources its picking up), or press it and hold it again to get to the second city mode (which is the upper case L), which will only alert and show visible indications for only those it thinks are real. I don't recall if the city modes operate only on the X-band or both X and K-band signals.
I've got a 1995 Valentine-1 and a year 2000 Valentine-1. They BOTH will pick up supermarket door openers and RF-based motion sensors, AS THEY SHOULD - as all door openers and RF-based motion sensors operate on the same frequencies as police radar ("field disturbance sensors", on 10.525 GHz for X-band, 24.150 GHz for K-band, 33.4 - 36.0 GHz range for Ka-band); most door openers and RF-based motion sensors are on X-band (cheaper), but I've also found some security system motion sensors on K-band (at a high-end stereo shop). If your Valentine-1 does *not* pick up door openers or such internal RF-based (not IR-based) motion sensors, then there is something wrong.
One alternative you may have is to disable reception of any band you know is not used by police radar. I know for a fact/experience that there are no police departments in my area using X-band at all, so I've programmed my year 2000 V-1 to ignore X-band (the method to do so is on their web site). I'd do it for the 1995 vintage detector, but it doesn't support the programming. I use the 1995 one in my Durango, so I have a double-check to see if any local departments have gotten cheap and started using X-band again. You're mileage may vary on that one (as it is a significant risk to disable a band).