Tritium breeding is a critical component of any self-sustaining future fusion reactor. The liquid-metal eutectic PbLi is of particular interest as a tritium breeder material due to its favorable thermophysical and neutronic properties. One of the several remaining challenges facing PbLi breeder blankets is the need to design and validate a highly efficient tritium extraction system. The vacuum permeator is a promising extraction concept that utilizes tritium permeation through a highly permeable metal membrane. The Tritium Extraction eXperiment (TEX) is a forced-convection PbLi loop constructed to investigate tritium extraction from PbLi with vacuum permeators. Accurate thermal-hydraulic and tritium transport models are required to establish appropriate test matrices, predict experiment outcomes, and analyze data. However, the hydrogen transport properties of PbLi and permeator materials have large uncertainties. A database is collected and a parametric analysis is conducted on the effect of hydrogen transport material properties, including diffusivity of H in PbLi and the permeator, solubility of H in PbLi and the permeator, and the permeator surface recombination constant, on the expected tritium extraction efficiency for a vacuum permeator installed in TEX. Herein, we observe that the solubility of H in PbLi and the permeator and the recombination constant of the permeator have the largest effect on extraction efficiency.