The yardstick is indeed the light-travel time.
Gravitational waves really do change the time it takes for light to travel between two points. We use light travel-times to measure distances, thus we say that the distance between the points has changed.
If it feels counterintuitive for spacetime to be changing, that's good. It is outside our human experience and perception. The strongest gravitational waves ever observed by scientists passed through everyone who was alive in 2015. None of those people noticed before the instruments registered a detection.