© 2018 authors. Published by the American Physical Society.The SU(3) gauge-field propagators computed from the lattice have been exhaustively used in the investigation of the low-momentum dynamics of QCD, in a judicious interplay with results from other nonperturbative approaches, and for the extraction of fundamental parameters of QCD like ?MS as well. The impact of the discretization artifacts and their role in the extrapolation of the results to the continuum limit have not been fully understood so far. We report here about a very careful analysis of the physical scaling violation of the Landau-gauge propagators renormalized in the momentum subtraction scheme and the Taylor coupling, steering us towards an insightful understanding of the effects from discretization artifacts which makes therefore possible a reliable continuum-limit extrapolation.