The tensor analyzing power component, T20, of the γd→→π0d process in the photon energy range from 200 to 400 MeV is investigated. This work is motivated by the most recent and unique measurements from the VEPP-3 electron storage ring at the Budker Institute of Nuclear Physics in Novosibirsk, Russia. We point out a special sensitivity of T20 to the elementary γN→πN amplitude and to the realistic NN potential model adopted for the deuteron wave function at backward pion angles, especially in the region 90°<θ<150°. The estimated results for T20 are compared with the experimental data from VEPP-3 and a satisfactory agreement is obtained at incident photon energies below 375 MeV. At higher photon energies and extreme backward pion angles, the estimated results of T20 considerably underestimate the data.