The gas content of the complete compilation of Local Group dwarf galaxies (119 within 2Mpc) is presented using HI survey data. Within the virial radius of the Milky Way (224kpc here), 53 of 55 dwarf galaxies are devoid of gas to limits of M_HI_<10^4^M_{sun}_. Within the virial radius of M31 (266kpc), 27 of 30 dwarf galaxies are devoid of gas (with limits typically <10^5^M_{sun}_). Beyond the virial radii of the Milky Way and M31, the majority of the dwarf galaxies have detected HI gas and HI masses higher than the limits. When the relationship between gas content and distance is investigated using a Local Group virial radius, more of the nondetected dwarf galaxies are within this radius (85+/-1 of the 93 nondetected dwarf galaxies) than within the virial radii of the Milky Way and M31. Using the Gaia proper-motion measurements available for 38 dwarf galaxies, the minimum gas density required to completely strip them of gas is calculated. Halo densities between 10^-5^ and 5x10^-4^cm^-3^ are typically required for instantaneous stripping at perigalacticon. When compared to halo density with radius expectations from simulations and observations, 80% of the dwarf galaxies with proper motions are consistent with being stripped by ram pressure at Milky Way pericenter. The results suggest that a diffuse gaseous galactic halo medium is important in quenching dwarf galaxies, and that a Local Group medium also potentially plays a role.