We present a generalization of the diagrammatic pump-probe approach to coherent backscattering (CBS) of intense laser light for atoms with degenerate energy levels. We employ this approach for a characterization of the double scattering signal from optically pumped atoms with the transition $J_grightarrow J_e=J_g+1$ in the helicity preserving polarization channel. We show that, in the saturation regime, the internal degeneracy becomes manifest for atoms with $J_ggeq 1$, leading to a faster decrease of the CBS enhancement factor with increasing saturation parameter than in the non-degenerate case.