Hiding a Window when capturing screen content using MediaProjection

I'm using the MediaProjection API to capture screen content. However, my app also uses a non-application window (like a system alert dialog added directly to the WindowManager) as an overlay and this is something I want omitted (as if it was invisible) from the screen contents captured.

When I set the window as secure, this results in a black rectangle in place of the window.

Is there any way to capture screen contents as if the overlay window was not there at all?

EDIT: To be clear, I want the overlay window to be visible to the user but not captured.

from Hiding a Window when capturing screen content using MediaProjection