  The upper bounds that the LHC measurements searching for heavy resonances
beyond the Standard model set on the resonance production cross sections are
not universal. They depend on various characteristics of the resonance under
consideration, like its mass, spin, and its interaction pattern. Their validity
are also limited by the assumptions and approximations applied to their
calculations. The bounds are typically used to derive the mass exclusion limits
for the new resonances. In our work, we address some of the issues that emerge
when deriving the mass exclusion limits for the strongly coupled composite
$SU(2)_{L+R}$ vector resonance triplet which would interact directly to the
third quark generation only. We investigate the restrictions on the
applicability of the generally used limit-obtaining procedure to this
particular type of vector resonances. We demonstrate that, in this case, it is
necessary to consider the bottom quark partonic contents of the proton.
Eventually, we find the mass exclusion limits for this resonance triplet for
some representative subsets of the parameter space.
