Does gravitational time dilation influence the propagation of the change of gravitational field?

This article uses thought experiments and strict logical deductions to discuss the propagation the change of gravity field and find that all current gravity fields are generated some time before and they are not static but are constantly propagating. If there is a change of the gravity field of a celestial body, it takes time for this change to propagate before interacting with this another celestial body. However, for a binary black hole system, the positions of the two black holes constantly changes relative to each other, resulting in changes of the gravity fields of both black holes, and, it also takes time for the change of gravity field of one black hole to reach the other black hole. If gravitational time dilation governs, it takes forever for the change of the gravity field of one black hole to propagate across the event horizon of the other black hole and interact gravitationally with it. If so, one black hole will never be able to respond to the change of the location of the other black hole. This is impossible. Thus, gravitational time dilation should not have the same influence upon the propagation of the change of gravity field as it has on light.