The CALorimetric Electron Telescope (CALET) cosmic ray detector on the International Space Station (ISS) has been in operation since its launch in 2015. The main instrument, the CALorimeter (CAL), is monitoring the gamma ray sky from ∼ 1 GeV up to ∼ 10 TeV with a field-of-view of about 2 sr for more than three and a half years. In this paper, we describe the improvement on gamma ray analysis to reduce secondary gamma rays produced by interaction of cosmic rays with the ISS structures and the automated search system for transient gamma-ray events such as gamma ray bursts and flares of active galaxies, and set upper limits on gamma-ray emission from gravitational-wave event candidates reported by the LIGO/Virgo third observing run since 2019 April.