The collision-energy dependence of the state-resolved differential cross section at a specific backward-scattering angle for the reaction H + D2 --> D + HD is measured with the D-atom Rydberg "tagging" time-of-flight technique. The reaction was modeled theoretically with converged quantum scattering calculations that provided physical interpretation of the observations. Oscillations in the differential cross sections in the backward-scattering direction are clearly observed and are attributed to the transition-state structures that originate from the interferences of different quantized transition-state pathways.