High-quality cross sections for the reaction γd → π0 d have been measured using the CLAS at Jefferson Lab over a wide energy range near and above the η-meson photoproduction threshold. At backward c.m. angles for the outgoing pions, we observe a resonance-like structure near E γ = 700 MeV. Our model analysis shows that it can be explained by η excitation in the intermediate state. The effect is the result of the contribution of the N(1535)S 11-resonance to the amplitudes of the subprocesses occurring between the two nucleons and of a two-step process in which the excitation of an intermediate η-meson dominates.