We present a study of the effect of strong electron-phonon coupling on the levels of the D-5 term of Fe2+ in II-VI zinc-blende semiconductors. The nonperturbative approach leads to a dramatic decrease of the level spacings of the (5) Gamma(5) manifold of Fe2+ in a tetrahedral environment. The results allow us to propose a mechanism for those absorption lines in the excitation spectrum of Fe2+ in CdTe which are not attributed to zero-phonon lines deduced from crystal-field theory. It is also shown that transitions between the crystal-field split states of Fe2+ can be explained on the basis of mixing of 3d(6) states with odd-parity states of higher configurations.