The mechanism of anelastic deformation of metallic glasses is a fundamental issue of materials physics. A critical step toward atomic level understanding is the identification of measurable atomic level structural parameters that respond to anelastic deformation. We demonstrate that the electric-field-gradient tensor measured by means of 27Al nuclear magnetic resonance in glassy La50Ni15Al35 is such a parameter and it reveals that anelasticity induces atomic processes that lead to increases of local site symmetry at Al sites. Such atomic processes could play an important role in the reversible slow β process.