The SNO+ experiment collected data as a low-threshold water Cherenkov detector from September 2017 to July 2019. Measurements of the 2.2-MeV γ's produced by neutron capture on hydrogen were made using an Am-Be calibration source, for which a large fraction of emitted neutrons are produced simultaneously with a 4.4-MeV γ. Analysis of the delayed coincidence between the 4.4-MeV γ and the 2.2-MeV capture γ revealed a neutron detection efficiency that is centered around 50% and varies at the level of 1% across the inner region of the detector, which to our knowledge is the highest efficiency achieved among pure water Cherenkov detectors. In addition, the neutron capture time constant was measured and converted to a thermal neutron-proton capture cross section of 336.3-1.5+1.2mb.