Characterizing the deep-buried reservoir beneath complex overburden media remains a challenge for seismic inversion. Elastic full waveform inversion (EFWI) can recover the subsurface elastic properties with reasonably high resolution by fitting observed data. However, EFWI using high frequencies requires fine discretization for the whole computational domain, and thus, it is expensive. Target-oriented EFWI allows us focus the high-resolution inversion on a target reservoir to reduce the computational cost. Considering that hydrocarbon reservoirs often underlie shale formations, which typically exhibit transversely isotropic behavior, we account for anisotropy in the overburden in the elastic redatuming process. An overburden model with reasonably explained velocity and anisotropy allows the redatuming to reconstruct the virtual elastic data representing the scattering response for the target zone. We then conduct EFWI by using the redatumed data to estimate the P- and S-wave velocities in the target zone. A synthetic SEAM model is used to demonstrate the performance of the proposed inversion scheme and highlight the influence of anisotropy on the redatuming and the inversion results.