  A Kekul\'e bond texture in graphene modifies the electronic band structure by
folding the Brillouin zone and bringing the two inequivalent Dirac points to
the center. This can result, in the opening of a gap (Kek-O) or the locking of
the valley degree of freedom with the direction of motion (Kek-Y). We analyze
the effects of uniaxial strain on the band structure of Kekul\'e-distorted
graphene for both textures. Using a tight-binding approach, we introduce strain
by considering the hopping renormalization and corresponding geometrical
modifications of the Brillouin zone. We numerically evaluate the dispersion
relation and present analytical expressions for the low-energy limit. Our
results indicate the emergence of a Zeeman-like term due to the coupling of the
pseudospin with the pseudomagnetic strain potential which separates the valleys
by moving them in opposite directions away from the center of the Brillouin
zone. For the Kek-O phase, this results in a competition between the Kekul\'e
parameter that opens a gap and the magnitude of strain which closes it. While
for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the
Dirac cones are much closer in the supperlattice reciprocal space that in
pristine graphene, we propose strain as a control parameter for intervalley
scattering.
