Recently, an association between an optical transient, AT2020hur, and a repeating fast radio burst, FRB 20180916b, has been suggested, based on a strong positional coincidence on the sky and the temporal coincidence with one of the fast radio burst's activity periods (~6 days duration every ~16 days). This suggestion is explored further and tested in this paper, utilizing full-frame images from the Transiting Exoplanet Survey Satellite (TESS) across three of its observing periods in 2019 and 2020 (Sectors 18, 24, and 25). The discovery observations of AT2020hur took place between Sectors 18 and 24, within 5 days of the commencement of Sector 24 observations. The TESS observations cover at least six activity periods for the FRB. Thus, the TESS data provide excellent temporal coverage close in time to the discovery of AT2020hur and at known times of FRB activity and radio detection. From the TESS data, no evidence is found for repeating optical transients with the suspected emission timescale of ⪆1000 s.