  We revisit the calculation of the six-gluon remainder function in planar
$\mathcal{N} = 4$ super Yang-Mills theory from the strong coupling TBA in the
multi-Regge limit and identify an infinite set of kinematically subleading
terms. These new terms can be compared to the strong coupling limit of the
finite-coupling expressions for the impact factor and the BFKL eigenvalue
proposed by Basso et al. in arXiv:1407.3766, which were obtained from an
analytic continuation of the Wilson loop OPE. After comparing the results order
by order in those subleading terms, we show that it is possible to precisely
map both formalisms onto each other. A similar calculation can be carried out
for the seven-gluon amplitude, the result of which shows that the central
emission vertex does not become trivial at strong coupling.
