Disable a Checkmate Alarm System

Harry potter goblet movie. I've had a 1996 Honda Civic for the past three years and due to the cold weather, the battery finally died. I put a replacement battery in yesterday and the alarm system started going off, so I turned the ignition key to 'on' and hit the reset button below the dashboard. This turned the alarm (made by Checkmate) off.

Now I was under the impression that the alarm system had been disabled by the previous owner. I've had the car for the last three years and I've never heard the alarm go off. Now, whenever I unlock the door (manual locks) and open the door, the alarm goes off. My question is: was my car in some kind of alarm bypass mode for the past three years? If so, how can I get back to that mode? And if it comes down to it, how do I remove the alarm?

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EDIT: Got it, method #1 below. Thanks for cluing me in on 'valet mode.'