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We present a combined angle-resolved photoemission spectroscopy and low-energy electron diffraction (LEED) study of the prominent transition metal dichalcogenide IrTe$_2$ upon potassium (K) deposition on its surface. Pristine IrTe$_2$ undergoes a series of charge-ordered phase transitions below room temperature that are characterized by the formation of stripes of Ir dimers of different periodicities. Supported by density functional theory calculations, we first show that the K atoms dope the topmost IrTe$_2$ layer with electrons, therefore strongly decreasing the work function and shifting only the electronic surface states towards higher binding energy. We then follow the evolution of its electronic structure as a function of temperature across the charge-ordered phase transitions and observe that their critical temperatures are unchanged for K coverages of $0.13$ and $0.21$~monolayer (ML). Using LEED, we also confirm that the periodicity of the related stripe phases is unaffected by the K doping. We surmise that the charge-ordered phase transitions of IrTe$_2$ are robust against electron surface doping, because of its metallic nature at all temperatures, and due to the importance of structural effects in stabilizing charge order in IrTe$_2$.