This paper considers classical strings propagating in γ-deformed AdS3×S3 backgrounds generated by certain shift T-dualities accompanied (TsT) transformations on S3 and ADS3,respectively.It finds that the U(1) currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds generated by TsT transformations on both S3 and ADS3.Applying the TsT transformations,it derives the local Lax connections and the monodromy matrices in γ-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.