A backdraft damper is the best product to keep rodents out of dryer vents. Backdraft dampers come in a variety of styles, types and colors to coordinate with the appearance of a home.
A backdraft vent prevents rodents and other outside animals from entering a home. It only opens when the dryer is in use. The air from the vent does not attract rodents due to the sudden, strong airflow. Ensure the backdraft vent is a quality product to ensure it stays air tight when the dryer is not on.
Although vent screens look like they could help prevent rodents from entering the home, the screens can become clogged with lint. The link that clogs the screen could start a fire.