  A precise transit ephemeris serves as the premise for follow-up exoplanet
observations. We compare TESS Objects of Interest (TOI) transit timings of 262
hot Jupiters with the archival ephemeris and find 31 of them having TOI timing
offsets, among which WASP-161b shows the most significant offset of
-203.7$\pm$4.1 minutes. The median value of these offsets is 17.8 minutes,
equivalent to 3.6 $\sigma$. We generate TESS timings in each sector for these
31 hot Jupiters, using a self-generated pipeline. The pipeline performs
photometric measurements to TESS images and produces transit timings by fitting
the light curves. We refine and update the previous ephemeris, based on these
TESS timings (uncertainty $\sim$ 1 minute) and a long timing baseline ($\sim
10$ years). Our refined ephemeris gives the transit timing at a median
precision of 0.82 minutes until 2025 and 1.21 minutes until 2030. We regard the
timing offsets mainly originating from the underestimated ephemeris
uncertainty. All the targets with timing offset larger than 10$\sigma$ present
earlier timings than the prediction, which cannot be due to underestimated
ephemeris uncertainty, apsidal precision, or R$\o$mer effect as those effects
should be unsigned. For some particular targets, timing offsets are likely due
to tidal dissipation. Our sample leads to the detection of period decaying
candidates of WASP-161b and XO-3b reported previously.
