What is the proper way to unregister Activity lifecycle callbacks?
Simon was right about this. registerActivityLifecycleCallbacks doesn't require a matching call to unregisterActivityLifecycleCallbacks. As described in this SO question you can't detected when your application is being killed. So there is no "logical" place to unregister your callback. And even if there was, your Application instance is killed after the last Activity action takes place, and the killing of your Application kills the mActivityLifecycleCallbacks list which holds the reference to your callback anyway.
TL;DR - Don't worry about calling unregisterActivityLifecycleCallbacks, it's only there if you want to stop tracking Activity actions during your Application's normal lifecycle.