In this work, the scattering of a Rayleigh wave by a surface-breaking crack with faces in partial contact is investigated. The elastic properties of the crack faces in contact are modeled within the framework of the quasi-static approximation (QSA). Two different contact distributions are considered. The first distribution is uniform over the whole extent of the crack faces. In the second one, the contacts occur only in the proximity of the crack mouth. The gradient of the crack opening displacement (COD) caused by the incident wave is obtained by solving a system of uncoupled integral equations. An integration of the COD gradients over the crack depth yields the components of the COD. The reflection and the transmission coefficients, as well as the energy of the incident Rayleigh wave, which is carried away by the mode-converted bulk waves can be calculated by employing the COD components in conjunction with reciprocity theory. Contrary to the expectations based on the behavior of the reflection coefficient of a bulk wave at normal incidence on an imperfect interface of infinite extent, the reflection coefficient of a Rayleigh wave scattered by a partially closed surface-breaking crack is predicted to increase initially with the load applied to the crack faces. Experimental evidence supporting such a surprising behavior is also presented.