Primordial bubbles that possibly nucleate through quantum tunneling during inflation in a multidimensional potential might have left some relic detectable at the present time. These bubbles turn into black holes during the radiation era, which may account for the LIGO black holes, supermassive black holes, and may play an important role in dark matter. Typically, these black holes are surrounded by an energy deficit in the form of a spherical sound wave packet propagating outwards. In this work we study how this perturbation of the cosmic plasma dissipates before the time of recombination, leading to spectral distortions in CMB. We find that there may exist some rare regions on the last scattering surface containing huge black holes, which have produced potentially detectable point-like signals of µ-type distortions.