The phase is one of the fundamental properties of a wave that allows to control interference effects and can be used to efficiently encode information. We examine numerically a magnonic resonator of the Gires-Tournois interferometer type, which enables the control of the phase of spin waves reflected from the edges of the ferromagnetic film. The considered interferometer consists of a Py thin film and a thin, narrow Py stripe placed above its edge, both coupled magnetostatically. We show that the resonances and the phase of the reflected spin waves are sensitive for a variation of the geometrical parameters of this bilayerd part of the system. The high sensitivity to film, stripe, and non-magnetic spacer thicknesses, offers a prospect for developing magnonic metasurfaces and sensors.