We determine the reaction yd-dff amplitude taking into account two mechanisms: the impulse approximation (IA) and the produced pion rescattering (double scattering) on the spectator nucleon (DS). In the calculation we use the non-relativistic diagrams. Employing the factorization hypothesis for the elementary processes y N + yNir and pN-Nlr amplitudes and the deuteron form factors, we determine the spin structure of both the considered parts of the amplitude. The kinematical conditions at which the elementary process amplitudes should be calculated are discussed in detail.We take into account the Fermi motion of nucleons in the deuteron. We show that the method used (the DS effect calculation) is appropriate at small l r ' production angles, @<9W and results in better agreement between the measured and calculated cross section. However, at @>9W the DS contribution to the reaction amplitude significantly excess the IA contribution. At large 9 production angles, the DS amplitude calculation is rather ambiguous.