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.