  Primordial black holes (PBHs) are plausible dark matter candidates that
formed from the gravitational collapse of primordial density fluctuations.
Current observational constraints allow asteroid-mass PBHs to account for all
of the cosmological dark matter. We show that elastic scattering of a
cosmological gravitational wave background, these black holes generate spectral
distortions on the background of 0.3% for cosmologically relevant frequencies
without considering coherent scattering and 5% when the coherent enhancement is
included. Scattering from stellar objects induce much smaller distortions.
Detectability of this signal depends on our ultimate understanding of the
unperturbed background spectrum.
