  We discuss how tensor polarizations of gravitational waves can suffer Landau
damping in the presence of velocity birefringence, when parity symmetry is
explicitly broken. In particular, we analyze the role of the Nieh-Yan and
Chern-Simons terms in modified theories of gravity, showing how the
gravitational perturbation in collisionless media can be characterized by a
subluminal phase velocity, circumventing the well-known results of General
Relativity and allowing for the appearance of the kinematic damping. We
investigate in detail the connection between the thermodynamic properties of
the medium, such as temperature and mass of the particles interacting with the
gravitational wave, and the parameters ruling the parity violating terms of the
models. In this respect, we outline how the dispersion relations can give rise
in each model to different regions of the wavenumber space, where the phase
velocity is subluminal, superluminal or does not exist. Quantitative estimates
on the considered models indicate that the phenomenon of Landau damping is not
detectable given the sensitivity of present-day instruments.
