A possible explanation for the existence of the cuprate "pseudogap" state is that it is a d-wave superconductor without quantum phase rigidity. Transport and thermodynamic studies provide compelling evidence that supports this proposal, but few spectroscopic explorations of it have been made. One spectroscopic signature of d-wave superconductivity is the particle-hole symmetric "octet" of dispersive Bogoliubov quasiparticle interference modulations. Here we report on this octet's evolution from low temperatures to well into the underdoped pseudogap regime. No pronounced changes occur in the octet phenomenology at the superconductor's critical temperature Tc, and it survives up to at least temperature T approximately 1.5 Tc. In this pseudogap regime, we observe the detailed phenomenology that was theoretically predicted for quasiparticle interference in a phase-incoherent d-wave superconductor. Thus, our results not only provide spectroscopic evidence to confirm and extend the transport and thermodynamics studies, but they also open the way for spectroscopic explorations of phase fluctuation rates, their effects on the Fermi arc, and the fundamental source of the phase fluctuations that suppress superconductivity in underdoped cuprates.