DIAGNOSIS: That's the 'Content Awareness' feature, part of the Ambient Mode/Google TV setup. It's trying to be helpful by showing you info or controls when it detects paused content, but it gets annoying fast.
FIX: You need to dig into the Accessibility settings to turn it off. 1) Press the Quick Settings button (the gear icon) on your remote. 2) Go to System > Accessibility. 3) Scroll down to Content awareness and toggle it OFF. That should stop the pop-up banner from appearing every time you hit pause.
IF THAT DIDN'T WORK: There's a second, related setting. Go back to Quick Settings > System > Ambient Mode. Turn Ambient Mode OFF. This disables the whole 'smart' background system, which is often the root cause of those pop-ups and screen changes.
HEADS UP: Turning off Content Awareness might also disable some other 'helpful' features, like showing actor details when you pause. If you find you miss that, you can always go back and toggle it on, but the trade-off is the persistent assistant button.