A theoretical formalism based on the fully renormalized kinetic theory is applied to a diffusion-influenced pseudo-first order reaction kinetics of reversible bimolecular reaction A +BF reversible arrow C+B including unimolecular decay processes. Linear response of the system, initially at equilibrium, to a thermal perturbation is examined and a rate kernel equation for the reactant concentrations is derived. The rate kernel has a hierarchical structure and the propagator appeared in the kernel expression is truncated by a disconnected approximation. When the unimolecular reactions are turned off, the response of the system is found to be the effective irreversible survival probability. In this way, many-body complications inherent to the history of reactive pair creation are properly implemented in the description of the reversible kinetics. We compare the present theory with the other existing theories such as the rate equation, the superposition approximation, and the convolution approaches. In some limiting cases, results obtained from the present theory can be reduced to those from the existing theories. For the present reaction scheme, we found that the description of the above many-body complications in the present theory lead to the equivalent result as in the rate equation approach.