  Local distortions of the crystal structure and their influence on the
electronic structure, electron-phonon interaction, and superconductivity are
theoretically studied in the superconducting high-entropy alloy (HEA)
(TaNb)$_{0.67}$(HfZrTi)$_{0.33}$. Distortions of the crystal lattice are caused
by the relaxation of atomic positions and are studied in the twelve models of
supercells. The largest relative changes in the interatomic distances due to
relaxation reach 8\%. On average, local distortions tend to lower the density
of states at the Fermi level and significantly reduce the electron-phonon
coupling parameter $\lambda$. As a result, the calculated superconducting
critical temperature is reduced to about 50\% of the initial value, which shows
the strong impact of structural disorder on superconductivity in this prototype
high-entropy alloy. With the reduced value of $\lambda$, the theoretical $T_c$
is closer to the experiment for typical values of the Columomb pseudopotential
parameter $\mu^*$. The experimental $T_c$ can be reproduced by taking a
slightly enhanced $\mu^* = 0.176$, which leaves little room for the possibility
of suppression of superconductivity by disorder.
