Your question raises an interesting point, and it's worth noting that the conservation of energy and the existence of gravitational waves are not contradictory. Allow me to explain.
In the context of a conservative gravitational field, we refer to the gravitational potential energy associated with an object's position in the field. When an object moves within a conservative field, its total mechanical energy (kinetic energy + potential energy) remains constant as long as there are no external forces acting on it. This conservation of mechanical energy holds true for orbits in the absence of energy loss mechanisms.
However, the presence of gravitational waves introduces a mechanism by which energy can be radiated away from a system. Gravitational waves are produced by accelerating masses, such as orbiting bodies, and they carry energy away from the system as they propagate through spacetime. This radiation of energy causes the orbiting bodies to gradually lose energy, resulting in a slow decay of their orbits and eventual inspiral or collision.
So, while the conservative gravitational field itself conserves mechanical energy, the system as a whole (including the gravitational waves) can experience a net loss of energy. This energy loss is precisely what allows us to detect and observe gravitational waves in the first place.
The conservation of energy is still upheld when we consider the entire system, including both the objects generating gravitational waves and the waves themselves. The lost energy is simply transferred to the gravitational wave field. It's important to note that this energy loss is generally very small for typical astronomical systems, and it requires extremely sensitive detectors like LIGO to observe the effects of gravitational waves.
In summary, the existence of gravitational waves and their ability to carry away energy does not contradict the conservative nature of the gravitational field. The gravitational potential energy associated with an object's position is conserved within the framework of a conservative field, while the overall system, including gravitational waves, can experience energy loss through radiation.