[en] We consider the detection of changes in the surface impedance of a partially coated crack, which we infer from the shift in a target signature arising from a modified interior transmission eigenvalue problem. We study this problem in a general setting in which the properties of the scattering medium are encoded in a bounded linear operator T, and we provide sufficient conditions for T that imply desirable properties of the eigenvalues of this problem. We conclude by placing scattering by a partially coated crack into this general framework and investigating the sensitivity of the associated eigenvalues to changes in the surface impedance with a series of numerical examples. (paper)