How good of a description of the dark compact objects in our Universe is the vacuum Kerr geometry? Precision measurements of accreting matter in the deep infrared and gravitational-wave measurements of coalescing objects are finally providing answers to this question. We study the possibility of resonant excitation of the modes of a central object-taken to be very compact but horizonless-during an extreme-mass-ratio inspiral. We show that, for very compact objects, resonances are indeed excited. However, we find that the impact of such excitation on the phase of the gravitational-wave signal is negligible since resonances are crossed very quickly during inspiral.