Fluorescence quenching by reversible excitation transfer is studied for a pseudo first-order model allowing only geminate-type back transfers from the acceptor to the donor. For the theoretical treatment a diffusion-kinetic hierarchy approach is applied derived on the base of reactive many-particle equations. It is demonstrated that the obtained nonlinear system of rate and pair equations is in the low concentration limit kinetically equivalent to a description by generalized rate equations (non-Markovian approach). By introducing an effective forward transfer coefficient, analogous to the definition of phenomenological rate coefficients for other type reversible reactions, compact and physically transparent formulas for the evolution of donor and acceptor concentrations during the quenching process are derived. The fluorescence quenching constant is explicitely given for a contact transfer mechanism. It is shown that for longer range transfers the calculation of the fluorescence constant calculation results in the solution of an integral equation. Some analytically solvable limiting cases are indicated and especially a Forster-type transfer is discussed.