Gravitational-wave observatories become more sensitive with each observing run, increasing the number of detected gravitational-wave signals. A limiting factor in identifying these signals is the presence of transient non-Gaussian noise, which generates glitches that can mimic gravitational wave signals. Our work provides a quasi-physical model waveform for the four most common types of short transient glitches, which are particularly problematic in the search for high-mass black hole binaries. Our model has only a few, physically interpretable parameters: central frequency, bandwidth, phase, amplitude and time. We demonstrate the accuracy of this model by fitting and removing a large sample of glitches from a month of LIGO and Virgo data from the O3 observing run. We can effectively remove three of the four types of short transients. We finally map the ability of these glitches to mimic binary black hole signals.