Inelastic interactions of quantum systems with the environment usually wash coherent effects out. In the case of Friedel oscillations, the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in three-dimensional topological insulator Bi2Te3 there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens due to disorder. The amplitude of the splitting allows an evaluation of the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.