Wronskian-type formula for inhomogeneous $TQ$ equations

It is known that the transfer-matrix eigenvalues of the isotropic open Heisenberg quantum spin-1/2 chain with nondiagonal boundary magnetic fields satisfy a $TQ$ equation with an inhomogeneous term. We derive a discrete Wronskian-type formula relating a solution of this inhomogeneous $TQ$ equation to the corresponding solution of a dual inhomogeneous $TQ$ equation.