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GdBa2Cu3Oy coated conductors were annealed under external strain (strain-annealing). The residual strain after annealing was evaluated using synchrotron radiation. We found that the residual strain is changed by the strain-annealing. The volume fraction of the a-axis domains along the longitudinal direction is increased by compression-annealing and decreased by tension-annealing. In addition, the Jc value of the tension-annealed sample increases drastically below 70 K, although the Jc value is smaller than that of the as-received sample at 77.3 K for B//c. The peak of the angular dependent Jc at θ = 0°, which originates from the c-axis correlated pinning, for the strain-annealed sample is much smaller than that of the as-received sample. It is considered that the shrinking of the c-axis correlated pinning because of the reduction of the twin structure and the increase of carrier doping may be related to the change in Jc properties.