  We study the effect of a stochastic background of gravitational waves on the
gravitational lensing of the Cosmic Microwave Background (CMB) radiation. It
has been shown that matter density inhomogeneities produce a smoothing of the
acoustic peaks in the angular power spectrum of the CMB anisotropies. A
gravitational wave background gives rise to an additional smoothing of the
spectrum. For the most simple case of a gravitational wave background arising
during a period of inflation, the effect results to be three to four orders of
magnitude smaller than its scalar counterpart, and is thus undetectable. It
could play a more relevant role in models where a larger background of
gravitational waves is produced.
