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Tensor target spin asymmetries [Formula: see text] ([Formula: see text]=0,1,2) in the reaction [Formula: see text] are studied for photon energies from [Formula: see text]-threshold up to 1.5[Formula: see text]GeV with inclusion of rescattering effects. It is shown that the influence of rescattering effects on the tensor target spin asymmetries is sizable in the energy region near [Formula: see text]-threshold. At higher energies, much smaller influence of rescattering effects is seen. The sensitivity of the obtained results to the elementary pion photoproduction operator is investigated and a considerable dependence is found, in particular at forward pion angles. In addition, a comparison with results of other theoretical models is also given. The extracted spin asymmetries are compared with available experimental data and a qualitative agreement is obtained. The predictions presented here may be useful to interpret the recent measurements from the VEPP-3 electron storage ring.