We investigate the production ratios of the naturally occurring s-only nuclides ${}^{122-124}$Te by solving a nuclear network in the mass number $120\leqslant A\leqslant 124$ region under some conditions representing those in the helium–hydrogen inter-shell in low-mass AGB stars as well as those in the helium burning and the carbon burning phases in massive stars. We show that the electron-capture process on 123Te (the natural half-life $\gt {10}^{16}$ years) could proceed decisively fast during the late evolutionary phases of massive stars. We thus re-iterate and re-enforce the decades-old notion that detailed analysis of the relative ${}^{122-124}$Te abundances in due consideration of the selective 123Te depletion in massive stars would set a stringent constraint on the s-process modelings. We stress that the relative abundance ratios of ${}^{122-124}$Te in the solar system become quite difficult to decipher if the s-process in massive stars contributes significantly to the synthesis of nuclides in this intermediate A region.