There are two reasons why I would state this is correct, beyond the obvious fact that these waves are perfroming work all the time - as in holding us to earth, hydroelectric power, people falling down and not up etc.
One book that people like to use as a source of information is, "A Brief History of Time". On page 93, the last paragraph, it is stated that when gravitational waves leave an object they take energy away from that object.
I've used a horizontal beam to detect the formation and collapse of a gravitational field. Check it out on
Http://timebones.blogspot.com
You gotta believe.
Duane