… Two things can happen: Either the planet gets very, very close to the binary, suffering tidal disruption or being engulfed by one of the stars, or its orbit gets significantly perturbed by the binary to be eventually ejected from the system …

This could be described intuitively in my opinion as a repeated slingshot effect … the same way that would make so that tides on Earth push the Moon gradually further away while slowing down Earths’ rotation …