Do I need to call UnityEvent.RemoveListener() when exiting the app?

It seems to handle automatically when the app exits, but is there a need to call somewhere for proper execution or correct coding habits?

It shouldn’t be tied to any system audio control if that’s what you mean. Is this a mobile app?

The Listener object of Unity is independent, and just sends signal to your system audio. It exits with everything else, as far as I know.