Converged continuum discretized coupled-channel calculations of elastic-scattering differential cross sections for reactions induced by the $^{6}\mathrm{Li}$ projectile on the $^{144}\mathrm{Sm}$ target, at energies around the Coulomb barrier, are presented. The impact of the low-lying $\ensuremath{\alpha}$-deuteron resonant states in $^{6}\mathrm{Li}$ $(l=2,{J}^{\ensuremath{\pi}}={3}^{+},{2}^{+},{1}^{+})$ on those elastic angular distributions is quantified. This is done by two types of calculations, namely, (a) by omitting from the continuum energy spectrum all states where the resonances are constructed in the discretization process, and (b) by considering only the resonance discretized space. Dynamical polarization potentials are used for interpreting the effect of continuum couplings. Resonant couplings play a more significant role than nonresonance ones at back-scattering angles and at incident energies below the Coulomb barrier. However, their effect becomes weaker as the incident energy increases above the barrier energy.