We can use time-dependent, high-resolution spectra of nearby stars to measure precise radial velocities (RVs) of stellar reflex motion to infer the existence of exoplanets. However, the Earth’s atmosphere introduces telluric absorption features that contaminate the stellar spectra obtained with ground-based telescopes. Our project quantifies the systematic errors in RVs that result from telluric absorption, and explores data analysis strategies to mitigate them. In the first paper in this series, we quantified the bias in precise radial velocity measurements in the visible and near-infrared from the presence of tellurics in a simulated set of observations using a synthetic G type star. In this work, we simulate the impact of telluric RV systematics for a synthetic M dwarf star to assess the dependence on spectral type. RVs are more impacted by tellurics for M dwarfs than for G type stars. We attribute the relative increase of telluric systematics on M dwarf spectra to the increased overlap in wavelength of telluric lines and stellar Doppler information content.