Gravitational-wave (GW) scattering in the strong gravitational field is a central problem in GW lensing. Yet, the conventional treatment based on the asymptotic expansion suffers from divergences and encounters difficulties near the optical axis. In this work, we present a rigorous calculation of GW scattering by a Schwarzschild black hole (BH) within the BH perturbation theory. By placing the observer at a finite distance and abandoning the asymptotic expansion of radial wave functions, we obtain a well-convergent partial-wave description without invoking any regularization scheme, thereby naturally resolving the divergences of the partial-wave series and the Poisson spot. We numerically computed the scattered GW waveforms by reconstructing the full metric perturbation from the master variables, revealing the formation of the Poisson spot and pronounced wavefront distortions. A systematic comparison with the corresponding asymptotic treatment shows that it reproduces the main qualitative features at large scattering angles but becomes inaccurate in the forward-scattering region at the finite observer distances considered here. We further compare the frequency-domain transmission factors derived from the scattering formalism with those obtained from the Kirchhoff diffraction integral, finding significant discrepancies at high frequencies and in the off-axis region due to the latter’s neglect of long-range gravitational effects and polarization evolution. Our results establish a stable and physically transparent framework for GW scattering in strong-field regimes and provide a solid foundation for accurate modeling of GW lensing beyond standard approximations.