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Gravitational waves from binary neutron star merger events have shown unparalleled advantages in deciphering the stellar internal structure, yet it remains underexplored to seek clues about kaon meson condensations inside massive neutron stars through these events. To address this gap, this study examines the binary star inspiral processes with kaon meson condensations, employing various kaon meson potential wells to probe unique imprints in the inspiral gravitational waves. Our analysis reveals that the inspiral process of kaon meson condensation binary stars exhibits lower gravitational wave frequencies and shorter retarded times compared to traditional neutron stars. Furthermore, a deeper kaon meson potential well in these systems further shortens the inspiral duration time, resulting in distinctive gravitational waveforms and notable orbital phase deviations. These findings underscore the pivotal role of kaon meson condensations in modulating the inspiral gravitational waves, suggesting the inspiral gravitational waves could serve as a powerful tool for probing potential signals of kaon mesons within neutron stars.