A major question in galaxy formation is how the gas supply that fuels activity in galaxies is modulated by their environment. We use spectroscopy of a set of well-characterized clusters and groups at 0.4<z<0.8 from the ESO Distant Cluster Survey and compare it to identically selected field galaxies. Our spectroscopy allows us to isolate galaxies that are dominated by old stellar populations. Here we study a stellar-mass-limited sample (log(M*/M_{sun}_)>10.4) of these old galaxies with weak [OII] emission. We use line ratios and compare to studies of local early-type galaxies to conclude that this gas is likely excited by post-AGB stars and hence represents a diffuse gas component in the galaxies. For cluster and group galaxies the fraction with EW([OII])>5{AA} is f[OII]=0.08_-0.02_^+0.03^ and f[OII]=0.06_-0.04_^+0.07^, respectively. For field galaxies we find f[OII]=0.27_-0.06_^+0.07^, representing a 2.8{sigma} difference between the [OII] fractions for old galaxies between the different environments. We conclude that a population of old galaxies in all environments has ionized gas that likely stems from stellar mass loss. In the field galaxies also experience gas accretion from the cosmic web, and in groups and clusters these galaxies have had their gas accretion shut off by their environment. Additionally, galaxies with emission preferentially avoid the virialized region of the cluster in position-velocity space. We discuss the implications of our results, among which is that gas accretion shutoff is likely effective at group halo masses (logM/M_{sun}_>12.8) and that there are likely multiple gas removal processes happening in dense environments.