All MAST catalog holdings are available via a ConeSearch endpoint.
GALEX data are available via the standard MAST CS service,and an auxiliary service for GALEX data only.
This catalog includes Galex GR 6/7 data, thus including the closeout release, as described at https://galex.stsci.edu/GR6/.
The Galaxy Evolution Explorer (GALEX), a NASA Small Explorer mission, performed the first all-sky, deep imaging and spectroscopic ultraviolet surveys in space. The prime goal of GALEX was to study star formation in galaxies and its evolution with time.
All available missions are listed at http://archive.stsci.edu/vo/mast_services.html.