The presence of nonmagnetic impurities in a 2D “bad” metal depresses the superconducting Berezinskii–Kosterlitz–Thouless transition temperature while leaving the pairing energy scale unchanged. Thus the region of the pseudogap nonsuperconducting phase, in which the modulus of the order parameter is nonzero but its phase is random and which arises at the pairing temperature, is substantially bigger than for the clean system. This supports the premise that fluctuations in the phase of the order parameter can in principle describe the pseudogap phenomena in high-TcTc materials over a rather wide range of temperatures and carrier densities. The temperature dependence of the bare superfluid density is also discussed.