I think what the GP was stating here were two independent reasons why we would find it hard to know what would happen if a gravitational square-ish wave interac

I think what the GP was stating here were two independent reasons why we would find it hard to know what would happen if a gravitational square-ish wave interacted with spacetime: 1. spacetime is "stiff", and 2. there are no gravitational square-ish wave generators around to observe. The two things are kind of related, though. One "natural" way to create a square wave in nature, is to "interrupt" a material transmitting a sinusoid wave, at the peak of its transmittance. And one way to do that, is to break through the modulus of elasticity of the material transmitting the wave, such that it switches from the elastic-deformation domain (transmitting the wave) to the plastic-deformation domain (ripping apart.) Imagine a speaker cone tearing at the peak of a high-amplitude drum beat. The cone pushes "out" — and then doesn't push back "in", because instead the air behind it rips forward through it. The air created by the speaker cone wants to rush back "in", but now there's no longer a speaker cone acting as a waveguide for the inward flow, so the natural turbulence cancels out much of the "falling" energy of the wave, making it look much more like a square-wave drop. I believe that the GP is saying that, because spacetime has such a high effective "modulus of elasticity", we haven't yet observed any practical way to perturb so as to create the conditions that would generate a gravitational square wave.