The incoherent transition strength of the exotic �--e- conversion in the 208Pb nucleus is investigated by utilizing the continuum random-phase-approximation method, appropriate for the evaluation of the rate that goes to the continuum of the nuclear spectrum. We find that the contribution of resonances lying high in the continuum is not negligible. Special attention is paid to the detailed study of the pronounced 1- contribution that according to previous calculations, dominates the overall incoherent rate in about all the nuclear targets. The spurious center-of-mass admixture to the partial rate originating from the 1- excitations is explored, and its elimination is performed by correcting properly the dipole operators. The results found this way show that the greatest portion of the total 1- contribution to the incoherent rate is spurious.