I had a stereo system that was pre-amp out (amp was in the rear of the car).
So it was radio to AMP in rear to the speakers. Radio died, I bought a new one, no sound. I by-passed the amp in the rear, but it is just wire for that
as I did it my way, no cool little box.
It has 8 leads, front left, front right, rear left, and rear right maybe. Nothing on there that would indicate a transmitter I see (so skip the tin foil on head idea).
The relay, does look like a some pop eliminator (delay startup; see Oznog response), a some surface mount on it. In a metal box, no antenna, doubt it sends anything to anywhere but the speakers. If in the rear of the car, probably an amp bypass or conditioner of some kind. They are probably messing with you when you ask about it or they have no clue what it is but it fixes a problem with your radio.
Did they change the radio out and replace it with a different model?
If so you probably received a lesser model.
Maybe they want to steal your XM signal (kidding)
Another thought, maybe a fix for a future failing power antenna motor as the factory unit does not cut out in time?. Maybe a circuit to cut on and off the power antenna.. But 8 wires.. Best guess speaker related.
But I do not believe they are spying on you, rather fixing something.