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To investigate the imprint on the gravitational-wave emission from extreme mass ratio inspirals (EMRIs) in nonpure Kerr spacetimes, we have studied the kludge waveforms generated in highly accurate, numerically generated spacetimes containing a black hole and a self-gravitating, homogeneous torus with comparable mass and spin. In order to maximize their impact on the produced waveforms, we have considered tori that are compact, massive, and close to the central black hole, investigating under what conditions the LISA experiment could detect their presence. Our results show that for a large portion of the space of parameters the waveforms produced by EMRIs in these black hole-torus systems are indistinguishable from pure Kerr waveforms. Hence, a “confusion problem” will be present for observations carried out over a time scale below or comparable to the dephasing time.