A black hole binary consists of two black holes orbiting their barycenter. Gravitational waves make the pair lose the kinetic energy. The black holes eventually spiral into each other and merge into a larger black hole.
I don't have the level of understanding the exact process behind that. I know that celestial bodies may lose kinetic energy for reasons like tidal forces, collisions and gravitational perturbation of other bodies. Tidal forces may cause friction at the planet's crust and convert kinetic energy into heat. That is why, for instance the moon is tidally locked to Earth because tidal forces made it lose rotation energy that turned into heat.
The question is: Gravitational waves make the two black holes lose kinetic energy, but this energy is converted into what? If there is no other celestial body nearby that will disturb them, then where this energy goes to? Is it transferred to the space-time fabric?