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The quasi-periodic oscillations (QPOs) observed in the X-ray variability of both black hole (BH) and neutron star (NS) systems provide a tool for probing strong gravity and dense matter equations of state. Nevertheless, the mechanism of QPO modulation in NS systems, where the amplitudes of QPOs with frequencies approaching kHz range are very high in comparison to BH high-frequency QPOs, remains an unsolved puzzle. Relativistic ray tracing of photons emitted from the immediate vicinity of compact objects has, to date, been used to investigate various mechanisms that explain the observed weak BH QPOs. However, it has not been applied to model the NS QPO signal, which requires incorporating the NS surface and a bright boundary layer (BL) on it. Here, we explore the QPO modulation mechanisms based on the BL obscuration. Using simplified models of axisymmetric oscillations of thick accretion discs (tori), we demonstrate that the disc oscillations drive the high NS QPO amplitudes through BL obscuration, which is relevant especially for vertical oscillations. We also demonstrate that obscuration effects enable the observability of the Keplerian frequency in the case of discs that decay due to instabilities., Comment: 10 pages, 5 figures, accepted for publication in The Astrophysical Journal