Motivated by a recent experiment by Bergeal et al., we reconsider incoherent pair tunneling in a cuprate junction formed from an optimally doped superconducting lead and an underdoped normal-metallic lead. We study the impact of the pseudogap on the pair tunneling by describing fermions in the underdoped lead with a model self-energy that has been developed to reproduce photoemission data. We find that the pseudogap causes an additional temperature-dependent suppression of the pair contribution to the tunneling current. We discuss consistency with available experimental data and propose future experimental directions.