  Working within the post-Minkowskian approach to General Relativity, we prove
that the radiation-reaction to the emission of gravitational waves during the
large-impact-parameter scattering of two (classical) point masses modifies the
conservative scattering angle by an additional contribution of order $G^3$
which involves a high-energy (or massless) logarithmic divergence of opposite
sign to the one contained in the third-post-Minkowskian result of Bern et al.
[Phys. Rev. Lett. {\bf 122}, 201603 (2019)]. The high-energy limit of the
resulting radiation-reaction-corrected (classical) scattering angle is finite,
and is found to agree with the one following from the (quantum) eikonal-phase
result of Amati, Ciafaloni and Veneziano [ Nucl. Phys. B {\bf 347}, 550
(1990)].
