Mute a listener
There should be a way to mute a listener, so when you have a pop-up with it's own listener that will make the previously active listener, if the user clicks off the pop-up window. Right now, you have to delete the listener, put up the pop-up and gather your data, then re-install the listener once the pop-up window is gone.
What I suggest is a new method that will temporarily mute a listener and can be unmuted when you want the background listener to be active again.
From what I see, I think it should be easily implemented and have no compatibility issues to previous apps that don't use it.
David Hockley commented
I think you can do what you require by putting a fullscreen rect with alpha = 0 behind the popup and in front of the previous window, and putting a listener on the rect that retuns true and so prevents the previous screen from receiving the event