  We obtain the reflected entropy for bipartite mixed state configurations of
two adjacent and disjoint subsystems at a finite temperature in finite-sized
non-gravitating reservoirs described by $CFT_2$s each coupled to two quantum
dots at their boundaries in the large central charge limit through a replica
technique. These field theory results are substantiated through a holographic
computation involving the entanglement wedge cross section in the dual bulk BTZ
black hole geometry truncated by two Planck branes. The two Planck branes are
the holographic duals of the quantum dots described by $AdS_2$ slices with JT
black holes. Our results reproduce the holographic duality between the
reflected entropy and the bulk entanglement wedge cross section in the context
of the $AdS_3/CFT_2$ correspondence. Subsequently we analyze the behaviour of
the holographic Markov gap between the reflected entropy and the mutual
information for different scenarios involving the subsystem sizes and time.
