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Two-dimensional topological materials have generated a lot of excitement as systems potentially exhibiting quantum spin Hall (QSH) effect, ballistic 1D transport, and helical edge modes. Monolayer 1T'-WTe₂ has been demonstrated to be both a QSH insulator and a superconductor upon doping using electronic transport and photoemission spectroscopy on single crystal flakes and epitaxial films. Atomically-resolved scanning tunneling microscopy (STM) also demonstrated clear edge states on WTe₂ monolayer islands. Here, we report the first STM study of monolayer 1T'-WTe₂ with in-situ tuning of carrier concentration using back-gating. We demonstrate band structure changes in response to doping and back-gating and use first principle calculations to explain the observed effects.