Reiner Gamma is a prime target for low-orbiting spacecraft or even surface-landed missions in the near future. The region hosts a prominent lunar swirl that is co-located with a strong and well-structured magnetic anomaly. We simulate and discuss Reiner Gamma's near-surface plasma environment at different altitudes above the lunar surface using the fully kinetic particle-in-cell code iPIC3D. The input magnetic field model is based on orbital-altitude observations from the Kaguya and Lunar Prospector missions. We develop eight simulation cases, representing the distinct plasma regimes Reiner Gamma is exposed to along a typical orbit, including different solar wind incidence angles and the magnetosheath crossing. We show that the plasma environment is vastly different at different altitudes and depends critically on the upstream plasma parameters, consistent with the predictions of the solar wind standoff model. Our work helps to define measurement requirements for a possible future low-orbiting or lander mission to the Reiner Gamma area or similarly magnetized regions of the lunar surface.