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By using the Continuum RPA (CRPA) method, the incoherent transition strength of the exotic μ−−e− conversion in nuclei is investigated. The question whether excited nuclear states lying high in the continuum give an important contribution to the incoherent rate is addressed. Results for 40Ca are compared with those obtained previously for 208Pb. For both nuclei we then investigate in detail the admixture of spurious components in the rate coming from 1− excitations, within the self-consistent CRPA with Skyrme interactions as well as within a less consistent version. We employ and compare two methods for removing the spurious strength: the use of effective operators, as done in a previous work for 208Pb, or simply the exclusion of the spurious state appearing close to zero energy. In all cases, the correction achieved is quite large.