The CALorimetric Electron Telescope (CALET) was launched in August 2015 and installed on the International Space Station (ISS) Japanese Experiment Module Exposed Facility. Alongside the primary science targets of GeV—TeV energy cosmic-ray electrons and cosmic-ray hadrons up to PeV energies, CALET is sensitive to gamma rays from 1 GeV up to 10 TeV, limited by statistics. Access to energies below 10 GeV is enabled by a dedicated low-energy gamma (LE-γ) trigger which is active only at low geomagnetic latitudes. In this work we review the analysis of gamma-ray events collected with this trigger including the mitigation of a secondary photon background from cosmic-ray interactions with ISS structures in the CALET field-of-view, the observation of persistent galactic and extragalactic sources, and the detection of emission from the quiescent Sun.