We report experimental results on the action of selected local environments on the fidelity of the quantum teleportation protocol, taking into account non-ideal, realistic entangled resources. Different working conditions are theoretically identified, where a noisy protocol can be made almost insensitive to further addition of noise. We put to test these conditions on a photonic implementation of the quantum teleportation algorithm, where two polarization entangled qubits act as the entangled resource and a path qubit on Alice encodes the state to be teleported. Bobs path qubit is used to implement a local environment, while the environment on Alices qubit is simulated as a weighed average of different pure states. We obtain a good agreement with the theoretical predictions, we experimentally recreate the conditions to obtain a noise-induced enhancement of the protocol fidelity, and we identify parameter regions of increased insensibility to interactions with specific noisy environments.