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By construction, the speed of light and GW is always the same and equals $c$ in "vacuum", i.e. in the space outside the matter and regardless the gravity force. However within matter things change both for the speed of light and for GW because of adjoint action of all sources.
See this comment. In the first link you will find what is a coordinate speed in the frame of linearized GR and the GW metrics. It is compatible with STR.
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