We present atomic hydrogen (HI) observations using the Robert C. Byrd Green Bank Telescope along the lines-of-sight to 27 low surface brightness (LSB) dwarf galaxy candidates discovered in optical searches around M101. We detect HI reservoirs in 5 targets and place stringent upper limits on the remaining 22, implying that they are gas poor. The distances to our HI detections range from 7 Mpc --150 Mpc, demonstrating the utility of wide-bandpass HI observations as a follow-up tool. The systemic velocities of 3 detections are consistent with that of the NGC~5485 group behind M101, and we suggest that our 15 non-detections with lower distance limits from the optical are associated with and have been stripped by that group. We find that the gas richnesses of confirmed M101 satellites are broadly consistent with those of the Milky Way satellites, as well as with those of satellites around other hosts of comparable mass, when survey completeness is taken into account. This suggests that satellite quenching and gas stripping proceeds similarly around halos of similar mass, in line with theoretical expectations.