  During the conference "Teleparallel Universes in Salamanca", we became aware
of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 99
(2019) 064006] in which some criticisms on the interpretation of teleparallel
gravity as a gauge theory for the translation group were put forward. This
triggered a discussion about the arguments on which those criticisms were
based, whose output is described in the present paper. The main conclusion is
that, to a great extent, those arguments are incorrect, and lack mathematical
and physical support.
