The scattered teleseismic body waves have been used intensively to characterize the receiver-side lithospheric structures. The routinely used ray-theory-based methods have their own limitations to image complex structures and tackle strong heterogeneities. The newly developed wave-equation based, passive-source reverse time migration (RTM) approach can overcome such limitations. To date, passive-source RTM has been developed only for isotropic media. However, at least to the first-order, most lithospheric structures possess effective transverse isotropy with spatially variable symmetry direction. It is important to know how if we image the lithospheric discontinuities when seismic anisotropy is treated in an incorrect way. In this paper, we investigate the influence of elastic anisotropy on teleseismic P-to-S conversion at the lithospheric discontinuities and gain insights to explain why an isotropic RTM may fail to focus the converted wavefields from the perspective of relative arrival time variations with backazimuth and shear wave splitting. Accordingly, we extend the passive-source RTM approach for imaging three-dimensional (3-D) lithospheric targets possessing transverse isotropy from the following two aspects: First, the teleseismic recordings with direct P and converted S phases are reverse-time extrapolated using rotated staggered grid (RSG) pseudo-spectral method which can tackle strong heterogeneity and transverse isotropies with symmetry axes in arbitrary direction; Second, the backward elastic wavefields are efficiently decomposed into vector anisotropic P and S modes to support accurate imaging. Two synthetic tests with hierarchical complexities reveal the significance of appropriate treatment of seismic anisotropy in passive-source RTM to characterize the receiver-side fine-scale lithospheric structures.