I have Netflix on my PS3 and when you pause you only get the noisy overlay after idling for 10 seconds or so. I press UP on the DPAD and it goes away, as UP does nothing if your focus is on the pause/play button. You can do it with SELECT too, it's also a dead key.

I am using a box (Android TV) and was finally able to remove the overlay by pressing the "back" button on my remote. Not exactly obvious, and not what I would call a good User eXperience.