Bosonic cascade lasers are terahertz (THz) lasers based on stimulated radiative transitions between bosonic condensates of excitons or exciton–polaritons confined in a trap. We study the interaction of an incoming THz pulse resonant in frequency with the transitions between neighboring energy levels of the cascade. We show that at certain optical pump conditions the cascade becomes transparent to the incident pulse: it neither absorbs nor amplifies it in the mean-field approximation. The populations of intermediate levels of the bosonic cascade change as the THz pulse passes, nevertheless. In comparison, a fermionic cascade laser does not reveal any of these properties.