First, we shoot a collection of particles (let's exclude gravitons from these, just for the sake of clarity) through a large region of spacetime in which the stress-energy tensor is zero and make them impact on a screen somewhere far away. A pattern will emerge.
Then we do the same with a second collection of particles (as much as possible identical to the first collection) but this time a gravitational wave is present.
We can vary a number of things. We can choose different particles (from photons to atoms). We can let the momenta of the particles have different angles (though they all are moving parallel wrt each other) wrt the direction in which the gravitational wave propagates. The same can be done but wrt to the screen. You can also vary the distance between the screen and the wave. The same can be done for the source of particles. For sure there will be different patterns visible in both cases. For example when the screen is placed far enough. Or not? Is it possible to detect gravitons with this construction (or, equivalently, to rule them out)?