This note attempts to reinterpret previous results on the dispersion of wind-induced inertial waves by a geostrophic barotropic jet in the ocean. The approach is to consider the jet vorticity influence on the different baroclinic modes using a vertical normal mode expansion. Numerical and analytical analysis of the linear equations shows that vorticity effects on a single baroclinic mode strongly depend on the ratio of its Rossby radius and the length scale of the geostrophic vorticity: trapping of the near-inertial energy occurs when this ratio is small. When this ratio is of order one, inertial waves are almost unaffected by the geostrophic vorticity because dispersion efficiently overcomes the jet vorticity effects. A 2-D primitive-equation model is used to examine the scattering of wind-induced inertial waves in realistic situations. Results indicate that contribution of the lowest baroclinic modes, unaffected by the jet vorticity, explain some striking features reported in previous studies as the downward phase propagation of near-inertial waves in the positive vorticity region.