Gravitational waves are on the same footing as electromagnetic waves - they are lightlike processes, propagating with speed of light c.
For all fundamental problems concerning time, we may not forget to have a look at the corresponding proper time. The proper time of lightlike processes is zero, their spacetime interval is empty. Observers are synchronizing the (zero) proper time of the observed process with the proper time of their own clock, and they get coordinate time. All lightlike processes are measured by observers to happen with velocity c, or more precisely, with velocity +c.
We don't know yet about processes which are moving backwards in time (that means which are moving against the direction of our own time arrow). The ideal candidates for processes moving backwards in time would be antiparticles, but it seems that such a presumption cannot be confirmed by experiment.
However, if we imagine that such an "antimatter observer" moving backwards in time would exist, this observer would measure lightlike processes as happening with a velocity of +c from his point of view (according to the second postulate of special relativity), that means -c from our point of view (opposite to the direction of our time arrow).
As a result we can say that light is interacting with matter in our direction, and if it would interact with some antimatter moving back in time, it could do so only in the opposite direction. However, as I said, no processes moving backwards in time are currently known.