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Using ultraviolet (UV) light curves, we constrain the circumstellar environments of 1080 Type Ia supernovae (SNe Ia) withinz< 0.5 from archival Galaxy Evolution Explorer (GALEX) observations. All SNe Ia are required to have pre- and post-explosion GALEX observations to ensure adequate subtraction of the host-galaxy flux. Using the late-time GALEX observations, we look for the UV excess expected from any interaction between the SN ejecta and circumstellar material (CSM). Four SNe Ia are detected near maximum light, and we compare the GALEX photometry to archival data. However, we find that none of our targets show convincing evidence of CSM interaction. A recent Hubble Space Telescope (HST) survey estimates that ∼6% of SNe Ia may interact with distant CSM, but statistical inferences are complicated by the small sample size and selection effects. By injecting model light curves into our data and then recovering them, we constrain a broad range of CSM interactions based on the CSM interaction start time and the maximum luminosity. Combining our GALEX nondetections with the HST results, we constrain occurrence of late-onset CSM interaction among SNe Ia with moderate CSM interaction, similar to that observed in PTF11kx, tof_CSM≲ 5.1% between 0 and 500 days after discovery and ≲2.7% between 500 and 1000 days after discovery at 90% confidence. For weaker CSM interactions similar to SN 2015cp, we obtain limits of ≲16% and ≲4.8%, respectively, for the same time ranges.