  The increasing sensitivity of gravitational-wave detectors has brought about
an increase in the rate of astrophysical signal detections as well as the rate
of "glitches"; transient and non-Gaussian detector noise. Temporal overlap of
signals and glitches in the detector presents a challenge for inference
analyses that typically assume the presence of only Gaussian detector noise. In
this study we perform an extensive exploration of the efficacy of a recently
proposed method that models the glitch with sine-Gaussian wavelets while
simultaneously modeling the signal with compact-binary waveform templates. We
explore a wide range of glitch families and signal morphologies and demonstrate
that the joint modeling of glitches and signals (with wavelets and templates
respectively) can reliably separate the two. We find that the glitches that
most affect parameter estimation are also the glitches that are well modeled by
such wavelets due to their compact time-frequency signature. As a further test,
we investigate the robustness of this analysis against waveform systematics
like those arising from the exclusion of higher-order modes and spin-precession
effects. Our analysis provides an estimate of the signal parameters; the glitch
waveform to be subtracted from the data; and an assessment of whether some
detected excess power consists of a glitch, signal, or both. We analyze the
low-significance triggers (191225_215715 and 200114_020818) and find that they
are both consistent with glitches overlapping high-mass signals.
