In this report the model-independent effective field theory phenomenology is used to parameterize the anomalous couplings in the Lagrangian with higher-dimensional operators. Setting limits on the operator's coefficients (EFT coupling constants) leads to new physics constraints. The decomposition technique of MC event generator MG5_aMC is used to produce events corresponding separate terms of the full amplitude. In the classical version of setting these limits, all background processes are considered as non-depending on coefficients. However in general case one or several backgrounds can be affected by non-zero EFT coupling constants. This report presents the way of accounting such background impact in limits setting. As an example the electroweak $Z\gamma$ production is considered, since this process is extremely sensitive to anomalous quartic gauge couplings. As a result the limits on the EFT coefficients $f_\text{T0}$ and $f_\text{M0}$ were obtained with accounting of the possible new physics in the electroweak $W\gamma$ production background, which are 1% and 5% tighter respectively than classical ones.