It's possible to move an object, and return it to its original location, without expending energy. Ocean waves do this all the time.
Based on conservation of energy, I would assume that friction can weaken a gravitational wave by turning some of its energy into heat.
Though if we're talking about permanently changing the location of an object, that theoretically requires a negligible amount of energy... reminds me of the magic drive in https://qntm.org/frontier