  Recently, we constructed the specific solution to the second-order
cosmological perturbation theory, around any
Friedmann-Lemaitre-Robertson-Walker (FLRW) background filled with dust matter
and a positive cosmological constant. In this paper, we use the Cosmicflows-4
(CF4) sample of galaxies from the Extragalactic Distance Database to constrain
this metric tensor. We obtain an approximation to the local matter distribution
and geometry. We numerically solve for null geodesics for randomly distributed
mock sources and compare this model with the Lemaitre-Hubble constant inferred
from the observations under the assumption of perfect isotropy and homogeneity.
We conclude on effects of realistic inhomogeneities on the luminosity distance
in the context of the Hubble tension and discuss limitations of our approach.
