<p>Entanglement is the key feature that distinguishes a quantum game from its classical counterpart. In this direction, entangling operators and their role in quantizing a classical game have been a subject of interest lately. Using these operators, a modification to the much explored Eisert-Wilkens-Lewenstein (EWL) quantization scheme is proposed and studied. In the present work, this scheme is subjected to noise through amplitude damping mode, bit-flip noise, and a comparative study with a noiseless case is carried out. As a result, we find that in the absence of noise, the payoffs of the players are high and can be manipulated by an entangling operator. Whereas when the factor of noise is maximum, the payoff of the players reduces to zero, and more so, there is no role for an operator in such a condition. A leap from quantum to classical game must then occur through noise (at least in the case of amplitude damping), as the maximum noise kills the effect of entanglement. However, such an observation depends on the nature of the noisy channel. In the case of a bit-flip channel, the noise actually favors the players’ payoffs, albeit still depending on entanglement. The results presented in this work display the prowess of the modified EWL scheme.</p>