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The constructive and destructive interference in different layers of the James Webb Space Telescope (JWST) Mid-Infrared Instrument (MIRI) detector arrays modulate the detected signal as a function of wavelength. Additionally, sources of different spatial profiles show different fringe patterns. Dividing by a static fringe flat could hamper the scientific interpretation of sources whose fringes do not match that of the fringe flat. We find point source fringes measured by the MIRI Medium-Resolution Spectrometer (MRS) to be reproducible under similar observing conditions. We want, thus, to identify the variables, if they exist, that would allow for a parametrization of the signal variations induced by point source fringe modulations. We do this by analyzing MRS detector plane images acquired on the ground. We extracted the fringe profile of multiple point source observations and studied the amplitude and phase of the fringes as a function of field position and pixel sampling of the point spread function of the optical chain. A systematic variation in the amplitude and phase of the point source fringes is found over the wavelength range covered by the test sources (4.9-5.8 $μ$m). The variation depends on the fraction of the point spread function seen by the detector pixel. We identify the non-uniform pixel illumination as the root cause of the reported systematic variation. We report an improvement after correction of 50% on the 1$σ$ standard deviation of the spectral continuum. A 50% improvement is also reported in line sensitivity for a benchmark test with a spectral continuum of 100 mJy. The improvement in the shape of weak lines is illustrated using a T Tauri model spectrum. Consequently, we verify that fringes of extended sources and potentially semi-extended sources and crowded fields can be simulated by combining multiple point source fringe transmissions.