  We consider the reaction g+d -> pi+d in a wide energy range around and above
the eta-meson photoproduction threshold at backward CM angles of the outgoing
pion. Our theoretical analysis is essentially motivated by the recent
measurements of the CLAS Collaboration at Jefferson Lab, where this kinematical
region of the reaction has been thoroughly studied for the first time and a
cusps in the energy dependence of the differential cross section in the region
of Eg = 600-800 MeV has been observed. Our preliminary and qualitative
analysis, based on single- and double-scattering diagrams, shows that the
observed structure can be explained by the contribution of the
double-scattering diagram with intermediate production of the eta meson. The
effect, to a considerable extent, is formed due to the contribution of N(1535)
resonance to the amplitudes of subprocesses on the nucleons.
