Impact on the RV trend from template matching after creating a telluric mask with different thresholds for the rejection of telluric-contaminated regions. The thresholds were applied to the same transmittance spectrum, generated through Telfit (Gullikson et al. 2014). Each row represents different nights of τ Ceti, chosen from within our subset specified in Table A.2. Left: residuals to the CCF RVs, color-coded based on the transmittance threshold; Right: slope of a first-degree polynomial adjusted to the residuals as a function of the transmittance threshold.