  We investigate the interaction between the cosmological relic neutrinos, and
primordial gravitational waves entering the horizon before the electroweak
phase transition, corresponding to observable frequencies today nu_0 <= 10^-5
Hz. We give an analytic formula for the traceless transverse part of the
anisotropic stress tensor, due to weakly interacting neutrinos, and derive an
integro-differential equation describing the propagation of cosmological
gravitational waves at these conditions. We find that this leads to a decrease
of the wave intensity in the frequency region accessible to the LISA space
interferometer, that is at the present the most promising way to obtain a
direct detection of a cosmological gravitational wave. The absorbed intensity
does not depend neither on the perturbation wavelength, nor on the details of
neutrino interactions, and is affected only by the neutrino fraction f_nu. The
transmitted intensity amounts to 88% for the standard value f_nu=0.40523. An
approximate formula for non-standard values of f_nu is given.
