I'd ask them if I can install another one on the back door. If they're giving me free money, who am I to judge their motivation?
Disclaimer: I hate car alarms with a vengeance. I think if a car alarm sounds and does not shut down within ten minutes (automatically or owner's intervention), there should be a large fine (I'd say the value of the car).
You should adjust the car alarm's settings. If you don't, and you happen to live in my neighbourhood, I have a stack of bricks in my back yard, one of which will just about fit through that hole in your windshield.