CO and CO₂ are among the most commonly monitored gases. However, the currently available semiconductor sensors require heating to ∼400 °C in order to operate effectively. This increases the power demand and shortens their lifespan. Consequently, new material prospects are being investigated. The adoption of novel two-dimensional layered materials is one of the pursued solutions. MoS₂ and MoTe₂ sheets have already been shown sensitive to NO₂ and NH₃ even at room temperature. However, their response to other compounds is limited. Hence, this work investigates, by employing density functional theory (DFT) calculations, the doping of Al, Si, P, S, and Cl atoms into the Te vacancy of MoTe₂, and its impact on the sensing characteristics for CO and CO₂. The computations predict that P doping significantly enhances the molecule-sheet charge transfer (up to +436%) while having only a little effect on the adsorption energy (molecular dynamics show that the molecule can effectively diffuse at 300 K). On the other hand, the doping has a limited impact on the adsorption of CO₂. The relative (CO/CO₂) response of P-doped MoTe₂ is 5.6 compared to the 1.5 predicted for the pristine sheet. Thus, the doping should allow for more selective detection of CO in CO/CO₂ mixtures.