Kagome metals possess peculiar optical spectra consisting of contributions from free charge carriers in a Drude-type response, localized carriers seen as a strongly temperature-dependent localization peak, and, in some cases, phonons displaying strong anomalies. The rare-earth kagome metal series, $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$, provides a marvelous playground to study the electronic properties of kagome metals in the presence of variable magnetic order. Here, we report temperature-dependent reflectivity studies on two members of the $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ family, ${\mathrm{GdMn}}_{6}{\mathrm{Sn}}_{6}$ (in-plane ferrimagnet) and ${\mathrm{TbMn}}_{6}{\mathrm{Sn}}_{6}$ (out-of-plane ferrimagnet), in a broad energy range (50--18 000 ${\mathrm{cm}}^{\ensuremath{-}1}$, equivalent to 6.2 meV--2.23 eV) down to 10 K. At high temperatures, a phonon mode at approximately 160 ${\mathrm{cm}}^{\ensuremath{-}1}$ is observed, which becomes screened out in ${\mathrm{TbMn}}_{6}{\mathrm{Sn}}_{6}$ below $\ensuremath{\sim}$150 K as the localization peak linearly passes through the mode. In ${\mathrm{GdMn}}_{6}{\mathrm{Sn}}_{6}$, the disappearance of the phonon is accompanied by the onset of saturation of the peak position, suggesting an unusual interplay between the two features.