When do two masses stop being gravitationally bound? Is that when each mass's relative speed exceeds the escape velocity of the other mass?
No, that can't be right: they could still end up in orbit - obviously gravitationally bound.
> “The memory is nothing but the change in the gravitational potential,” said Thorne, “but it’s a relativistic gravitational potential.” The energy of a passing gravitational wave creates a change in the gravitational potential; that change in potential distorts space-time, even after the wave has passed.
Gravitational waves are that energy.
Not to mention that there's no reason to assume conservation of energy still holds if the laws of physics simply change over time (which would be the case in the simplest possible theory were all interaction distances simply shrink over time).