Defect engineering in monolayer MoS₂ is a promising route to tune field-effect transistors (FETs), but the electronic response of defects in processed devices can be masked by contacts, substrate effects, adsorbates, and chemical passivation. Here, we irradiate MoS₂ FETs with low-energy 40 eV Ar⁺ ions to preferentially create sulfur vacancies (V_S) in the channel while minimizing substrate damage. We compare dark and illuminated electrical characterization with surface analysis and first-principles calculations. Dark transfer characteristics show an apparent robustness against irradiation up to moderate fluences, with pronounced degradation only at the highest fluence. Under 532 nm illumination, however, the photocurrent and light-induced photodoping decrease systematically with increasing ion fluence, revealing irradiation-induced changes that are hidden in standard dark measurements. Atomic force microscopy and X-ray photoelectron spectroscopy show substantial carbon-containing residues on processed devices even after extended cleaning. We propose that such residues may provide a reservoir for hydrocarbon-mediated passivation of sulfur vacancies. Density-functional-theory calculations provide a microscopic model consistent with this scenario: unsaturated V_S introduce in-gap states, H-C_S configurations suppress these states, and carbon substitution without hydrogen leaves defect states in the band gap. Our results highlight carbon-containing surface contamination as a key factor in interpreting defect engineering experiments on MoS₂ and related TMDC devices.