New interactions of neutrinos with a subdominant component of dark matter can prevent them from free streaming. As a result, the inflationary gravitational waves escape the damping by neutrinos and, with respect to the standard LCDM cosmology, there is enhancement of primordial gravitational wave amplitude and CMB B-modes on small scales. The effect on the CMB scalar acoustic oscillations is the absence of neutrino induced phase shift that is present in the standard LCDM cosmology with free streaming neutrinos. The dark neutrino interaction therefore shifts the acoustic oscillation features in the CMB temperature and E-mode polarization power spectra thus pushing the CMB inferred value of the Hubble constant higher, alleviating the Hubble tension. The inflationary CMB B-modes, if measured precisely with future experiments, are therefore a potential probe of new interactions beyond the standard model and can test this solution to the Hubble tension.