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The interaction effect between the surface states of a topological insulator (TI) and a STM-coupled Anderson impurity is studied by using equations of motion of the Green’s functions. Remarkably, we show that when a coupling between the Anderson impurity and the STM tip is included, the tunneling resonance and the Kondo peak can be tuned to be exactly at the Dirac point, by adjusting the impurity level and Fermi energy, such that the local density of states at the Dirac point is significantly enhanced. This is in contrast to the case of a STM-decoupled Anderson impurity, where both resonances are always fully suppressed at the Dirac point. Our finding suggests a pathway to experimentally control the fundamental properties of the electrons on a TI surface.