The absence of holelike Fermi pockets in the heavily electron-doped iron selenides (HEDISs) challenges the s_{±}-wave pairing originally proposed for iron pnictides, which consists of opposite signs of the gap function on electron and hole pockets. While the HEDIS compounds have been investigated extensively, a consistent description of the superconducting pairing therein is still lacking. Here, by in situ scanning tunneling spectroscopy and theoretical calculations, we study the effects of strong scatterings from nonmagnetic Pb adatoms on the epitaxially grown HEDIS, one-unit-cell FeSe/SrTiO_{3}(001). Systematic tunneling spectra measured on the Pb adatoms show comprehensive signals of quasiparticle bound states, which can be well explained theoretically within the sign-reversing pairing scenarios. The finding implies that, in addition to previously detected phonons, spin fluctuations play an important role in driving the Cooper pairing in FeSe/SrTiO_{3}(001). The sign reversal in the gap function we revealed here is a significant ingredient in a unified understanding of the high-temperature superconductivity in HEDISs.