We characterized the effects of telluric absorption lines on the radial velocity (RV) precision of stellar spectra taken through an iodine cell. To isolate the effects induced by telluric contamination from other stellar, instrumental, or numerical systematic RV noise, we extracted RVs from simulated iodine calibrated spectra of three RV standard stars regularly observed by Keck/HIRES. We add in water absorption lines according to measured precipitable water vapor (PWV) contents over a one-year period. We concluded that telluric contamination introduces additional RV noise and spurious periodic signals on the level of 10-20 cm/s, consistent with similar previous studies. Our findings show that forward modeling the telluric lines effectively recovers the RV precision and accuracy, with no prior knowledge of the PWV needed. Such a recovery is less effective when the water absorption lines are relatively deep in the stellar template used in the forward modeling. Overall, telluric contamination plays an insignificant role for typical iodine-calibrated RV programs aiming at ~1-2 m/s, but we recommend adding modeling of telluric lines and taking stellar template observations on nights with low humidity for programs aiming to achieve sub-m/s precision.
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