They have been offered white noise machines and movie tickets to mitigate the disturbance created by WestConnex construction, now some residents of Sydney's inner west are being sent earplugs.

Some residents in parts of the inner west near WestConnex construction sites say they have been affected by continual drilling, jack-hammering and concrete cutting for months.

While some of the most severely affected residents have been offered alternative accommodation during the construction period, those who don't meet the criteria are being provided with other noise mitigation strategies.

Inner West Council mayor Darcy Byrne described the earplug offer as "an insulting Band-Aid solution" in a post on his Facebook page accompanied by a picture of the plugs and letter from WestConnex.