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In this paper we investigate the impact of transient noise artifacts, or glitches, on gravitational- wave inference from ground-based interferometer data, and test how modeling and subtracting these glitches affects the inferred parameters. Due to their time-frequency morphology, broadband glitches cause moderate to significant biasing of posterior distributions away from true values. In contrast, narrowband glitches induce negligible biasing effects, due to distinct signal and glitch morphologies. We inject simulated binary black hole signals into data containing three occurring glitch types from past LIGO-Virgo observing runs, and reconstruct both signal and glitch waveforms using BayesWave, a wavelet-based Bayesian analysis. We apply the standard LIGO-Virgo-KAGRA deglitching pro- cedure to the detector data, which consists of subtracting from calibrated LIGO data the glitch waveform estimated by the joint BayesWave inference. We produce posterior distributions on the parameters of the injected signal before and after subtracting the glitch, and we show that removing the transient noise effectively mitigates bias from broadband glitches. This study provides a baseline validation of existing techniques, while demonstrating waveform reconstruction improvements to the Bayesian algorithm for robust astrophysical characterization in glitch-prone detector data.