Re: Complications
The effects of gravity on time has been known for nearly a century. Surprisingly the SI definition actually takes that into account; a measurement of (say) a second will be identical whether made on the surface of the Earth or in deep space; however an absolute comparison of the measurements will show a (very small) difference due to gravity-induced time dilation.
In order to detect gravity waves, they will need a network of four or more clocks equally distant from each other. One would then measure the absolute differences in the clock readings caused by gravity waves; by looking at the order in which the clocks drift back and forwards it becomes possible to determine the direction from which the gravity wave hit us.