The pressure-induced valence transition in TmTe was investigated by resonant inelastic x-ray scattering at the Tm L3 edge, a powerful probe of the rare-earth valent state. The data are analyzed within the Anderson impurity model which yields key parameters such as the Tm 4f-5d hybridization. In addition to the general tendency of the f electrons towards delocalization, we find a plateau in both the Tm valence and hybridization pressure dependences between 4.3 and 6.5 GPa which is interpreted in terms of an n-channel Kondo (NCK) screening process. This behavior is at odds with the usually continuous, single-channel Kondo-like f delocalization while being supported by the seminal calculations of the NCK temperature in Tm ion by Saso et al. Our study raises the interesting possibility that an NCK effect realized in a compressed mixed-valent f system could impede the concomitant electron delocalization.