What happens to gravity waves as they move through patches of space with different "timezones"? Gravity waves from a kilonova are affected by the distance thro

What happens to gravity waves as they move through patches of space with different "timezones"? Gravity waves from a kilonova are affected by the distance through space they have to travel but since they have no mass in themselves, they do not have their own "clock" and would not be affected by time differences? It's a "speed of causality" question that breaks my brain. Maybe that next-gen space interferometer (LISA) can help answer that, well if it's not cancelled, sigh, oh wait it's Europe-only project now so should happen https://en.m.wikipedia.org/wiki/Laser_Interferometer_Space_Antenna https://en.m.wikipedia.org/wiki/Laser_Interferometer_Space_A...