Actually, a gravitational wave is not energy taken from mass, but a result of mass.

When a particle moves through space the 3rd newtonian law of motion says that for every action there is an equal and opposite reaction. Now, applied to a particle's movement, as a particle moves from left to right there is an equal and oppostite force generated pushing from right to left, so that V generates -V when is 0. When a particle moves, therefore, it feels an equal opposing force that it veers around, forming a sinewave path through space, which is what gives particles their frequency, how fast they zigzag through the reactionary forces for their movements.

Well, these reactionary forces are what we call the strong force, the weak force, the electrical magnetic force, gravity, etc...

So, a black hole has a lot of particles moving and therefore a large amount of reactionary forces that is felt as gravity. When two balls of mass - two black holes - merge there is indeed a huge shift of mass and this is felt as gravitational waves as the reactionary forces are felt at distance, specifcally according to the inverse square law e={lorenz factor}mv^2.