Solar wind plasma interaction with lunar crustal magnetic fields is different than that of magnetized bodies like the Earth. Lunar crustal fields are, for typical solar wind conditions, not strong enough to form a (bow)shock upstream but rather deflect and perturb plasma and fields. Here we study the global effects of protons reflected from lunar crustal magnetic fields on the lunar plasma environment when the Moon is in the unperturbed solar wind. We employ a three-dimensional hybrid model of plasma and an observed map of reflected protons from lunar magnetic anomalies over the lunar farside. We observe that magnetic fields and plasma upstream over the lunar crustal fields compress to nearly 120% and 160% of the solar wind, respectively. We find that these disturbances convect downstream in the vicinity of the lunar wake, while their relative magnitudes decrease. In addition, solar wind protons are disturbed and heated at compression regions and their velocity distribution changes from Maxwellian to a non-Maxwellian. Finally, we show that these features persists, independent of the details of the ion reflection by the magnetic fields.