An inverse response matrix converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. This also results in extraction of intensity and energy distributions of multiply scattered events originating from interactions of 279 keV photons with thick targets of bronze. The observed pulse-height distributions are a composite of singly and multiply scattered events in addition to bremmstrahlung originating from slowing down of Compton and photo-electrons in thick targets. To evaluate the contribution of multiply scattered events, the spectrum of singly scattered events contributing to inelastic Compton peak is reconstructed analytically. The optimum thickness (saturation depth), at which the number of multiply scattered events saturate, has been evaluated in different energy bin meshes chosen for scintillation detector response unfolding. Monte Carlo calculations based upon the package developed by Bauer and Pattison (Compton scattering experiments at the HMI (1981), HMI-B 364, pp. 1-106) supports the present experimental results.