It's an infrared motion sensor. They're not like cameras -- they can only detect "movement" when something warm moves in front of them. It's probably part of the old security system, and if the system is disabled it's not "spying" on you. They're also used for automatic lights.
What is this thing?
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I know this is an older post, but I thought I'd chime in with my thoughts.
This looks like an IR motion detector. What it looks like to me, at least. It looks like something that would sense the rebound of ir light as it passes from one area of the room to the next... It could be part of a security system, that I'm not positive about - we've never had an ADT system, but we do use the motion of sensors for home security as well as automation.
(Source: we have motion sensors for our automated house.)