This is not true, and in fact there is a very famous thought experiment called the "sticky bead argument" that was pivotal in developing the consensus that gravitational waves are a real, physical effect and not just a "gauge" effect (an artifact of the coordinate system):
The OP might be making a more subtle point, but my understanding is they absolutely can do work. We can measure the deceleration of binary neutron stars with a rate predicted by the emission of gravitational waves. Deceleration == work.
However, we can also measure things that don’t do work, for example, a static magnetic field does no work on a charged particle (it cannot change its kinetic energy) but look at the swirls in a cloud chamber and it’s clear as day if there’s a magnetic field there.
I'm wrong on the work thing, but I don't think we can always regard deceleration as work, since that only works for Newtonian mechanics. Under GR there is an extra term in the equation allowing for acceleration without work.
https://en.wikipedia.org/wiki/Sticky_bead_argument
On the other hand, I definitely agree that gravitational waves are almost certainly too weak to cause any tectonic effects.