Illustration of the TDTM method. Panel a: segment of the VIS template spectrum of Wolf 294. The number M_k of exposure pixels that contribute to each template knot is color-coded. The red shaded wavelength ranges mark knots with M_k = 0. Panel b: one residual telluric spectrum F_n,i/S (λ_n,i) (black dots) after the division of the science spectrum by the template, and the best-fit telluric model (T(λ_n,i), green line) derived with molecfit. The red shaded wavelength ranges are excluded from the transmission model fit. Panel c: absolute residuals F_n,i/S(λ_n,i) – T(λ_n,i) of the fit. Panel d: CARMENES spectrum before (F_n,i, red line) and after (F_n,i/T(λ_n,i)) correction with the transmission model derived with molecfit (black line). Panel e: telluric free high S/N template spectrum of Wolf 294 (black line) built using 444 telluric absorption- corrected CARMENES observations. The order has a S/N of 2310.