In this paper, the SH-wave scattering by an orthotropic triangular soft hill settled on the underlying half-space was investigated using a half-space time-domain boundary element method to obtain a seismic ground response. The surface of the hill and its interface were only discretized by quadratic elements to elaborate on the computational model. First, a brief formulation of the method and the modified boundary integral equation with damping were presented. Then, the method was implemented in a developed DASBEM algorithm and analyzed as a verification example to compare with the literature and confirm the obtained results. Finally, an advanced numerical study was carried out to sensitize the key parameters of the model, including the isotropy factor, shape ratio of the hill, incident wave angle, and frequency content. The results showed that the proposed method had the powerful ability to create sharp corner features. Also, the orientation of the material texture of the triangular hill was extremely effective on the seismic ground response and changing the amplification patterns.