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Abstract The Zintl compound TlInTe₂is an intriguing material because of its outstanding thermoelectric properties at ambient pressure. Interestingly, it has recently been found that TlInTe₂exhibits a V-shape dependence of the superconducting critical temperature (T_c) under increasing pressure, which has been linked to the reversed behavior of the Raman active A_gphonon mode and anharmonic effects. In this study, we have performed first-principles calculations of the electron-phonon interactions and the superconducting properties of TlInTe₂in order to understand this unusual pressure-induced response. In contrast to experiment, we find a dome-shaped pressure-induced dependence ofT_cwith a maximum value of 0.23 K at 18 GPa, significantly lower than the experimental results. Electron doping has the potential to adjust theT_cto fall within the experimental range, but it necessitates considerably high levels of doping. Furthermore, our analysis of the phonon spectra and phonon lifetimes, including anharmonic effects, show that anharmonicity is unlikely to influence the superconducting properties of TlInTe₂. It remains an open question whether there is indeed an unusual V-shapeT_cdependence with pressure or whether the phonon-mediated theory of superconductivity used here breaks down in this system.