Do Gravitational Waves Leave an Imprint on Space?

We know gravitational waves leave an impact in stuff around the universe, right? Like if it goes through stuff, it leaves a little bit of energy because it had to squeeze it and stretch it. The question we're really asking is do gravitational waves leave a lasting imprint on space itself? In the 70s, people who were playing with the equations of general relativity discovered to their surprise that it should.