[en] The microscopic approach to quasielastic knock-out of clusters from atomic nuclei by fast hadrons is applied to develop a method to take into account distorting factors caused by rescattering of a hadron on those nucleons of the nucleus which do not form the virtual cluster and by interaction between the outgoing cluster and the remaining nucleus. The ⁶Li(p, pt)³He reaction with 1-GeV protons is used as an example to show that these factors can be totally taken into account in the multiple scattering theory. However, the distorting factors lead to a complicated dependence of cross sections not only upon the moduli of the momentum p transferred by the hadron and of the recoil momentum q but as well upon the angles between p and q