  In this work, we perform a holographic study to estimate the effect of
backreaction on the correlation between two subsystems forming the thermofield
double (TFD) state. Each of these subsystems is described as a strongly coupled
large-$N_c$ thermal field theory, and the backreaction imparted to it is
sourced by the presence of a uniform distribution of heavy static quarks. The
TFD state we consider here holographically corresponds to an entangled state of
two AdS blackholes, each of which is deformed by a uniform distribution of
static strings. In order to make a holographic estimation of correlation
between two entangled boundary field theories in presence of backreaction we
compute the holographic mutual information in the backreacted eternal
blackhole. The late time exponential growth of an early perturbation is a
signature of chaos in the boundary thermal field theory. Using the shock wave
analysis in the dual bulk theory, we characterize this chaotic behavior by
computing the holographic butterfly velocity. We find that there is a reduction
in the butterfly velocity due to a correction term that depends on the
backreaction parameter. The late time exponential growth of an early
perturbation destroys the two-sided correlation, whereas the backreaction
always acts in favour of it. Finally we compute the entanglement velocity that
essentially encodes the rate of disruption of correlation between two boundary
theories.
