Mass transfer across a liquid-repelling gas permeable membrane is influenced by the state(s) of the liquid-vapor interface(s) on the surface of the membrane, the pore geometry, and the solid-fluid interactions inside the membrane. By tuning the different local contributions, it is possible to enhance the temperature difference-driven mass flux across the membrane for a constant driving force. Non-equilibrium molecular dynamics simulations were used to simulate a temperature difference-driven mass flux through a gas permeable membrane with the evaporating liquid on one side and the condensing liquid on the other. Both sides were simulated for Wenzel- and Cassie-Baxter-like states. The interaction between the fluid and the solid inside the gas permeable membrane varied between the wetting angles of θ = 125° and θ = 103°. For a constant driving force, the Cassie-Baxter state led to an increased mass flux of almost 40% in comparison to the Wenzel state (given a small pore resistance). This difference was caused by an insufficient supply of vapor particles at the pore entrance in the Wenzel state. The difference between the Wenzel and Cassie-Baxter states decreased with increasing resistance of the pore. The condensing liquid-vapor interface area contributed in the same manner to the overall transport resistance as the evaporating liquid-vapor interface area. A higher repulsion between the fluid and the solid inside the membrane decreased the overall resistance.