Still not explaining it. If spacetime is stretched why doesn't light "speed up" to accommodate for it is what he's asking. I'm assuming it's because the speed of light is invariant to that.

Exactly. The speed of light in a vacuum is constant no matter how quickly/slowly your frame of reference is (Special Relativity). You can think of it as the space "stretching/shrinking" because of the gravitational wave, as that is how it looks from the point of view outside the experiment.

Another way to look at it is to change your reference to be internal to the experiment. You can imagine the experiment moving through space-time at a constant rate of speed. When the gravitational wave hits the experiment its movement through space-time changes an infinitesimal amount (faster than slower as the wave passes, or vice-versa). Since the speed of the light passing through space-time has not changed (due to special relativity), the difference between its start and end points can be used to measure the amount of change caused by the gravitational wave, essentially in the same way you can use a laser to measure the speed of a moving object relative to a stationary object. Only you are basically "bouncing" the laser off of the experiment itself to determine the change.