The FeTe parent compound for iron-superconductor chalcogenides was studied applying Mössbauer spectroscopy accompanied by ab initio calculations of electric field gradients at the iron nuclei. Room-temperature (RT) Mössbauer spectra of single crystals have shown asymmetric doublet structure commonly ascribed to contributions of over-stoichiometric iron or impurity phases. Low-temperature Mössbauer spectra of the magnetically ordered compound could be well described by four hyperfine-split sextets, although no other foreign phases different from Fe_1.05Te were detected by XRD and microanalysis within the sensitivity limits of the equipment. Density functional ab initio calculations have shown that over-stoichiometric iron atoms significantly affect electron charge and spin density up to the second coordination sphere of the iron sub-lattice, and, as a result, four non-equivalent groups of iron atoms are formed by their local environment. The resulting four-group model consistently describes the angular dependence of the single crystals Mössbauer spectra as well as intensity asymmetry of the doublet absorption lines in powdered samples at RT. We suppose that our approach could be extended to the entire class of Fe_1+ySe_1-xTe_x compounds, which contain excess iron atoms. (Figure presented.).