Subtracting glitches from gravitational-wave detector data during the third observing run

Data from ground-based gravitational-wave detectors contains numerous short-duration instrumental artifacts, called "glitches." The high rate of these artifacts in turn results in a significant fraction of gravitational-wave signals from compact binary coalescences overlapping glitches. In LIGO-Virgo's third observing run, $\approx 20\mathrm{\%}$ of signals required some form of mitigation due to glitches. This was the first observing run that glitch subtraction was included as a part of LIGO-Virgo-KAGRA data analysis methods for a large fraction of detected gravitational-wave events. This work describes the methods to identify glitches, the decision process for deciding if mitigation was necessary, and the two algorithms, BayesWave and gwsubtract, that were used to model and subtract glitches. Through case studies of two events, GW190424_180648 and GW200129_065458, we evaluate the effectiveness of the glitch subtraction, compare the statistical uncertainties in the relevant glitch models, and identify potential limitations in these glitch subtraction methods. We finally outline the lessons learned from this first-of-its-kind effort for future observing runs.