The DisplayLink Manager Application requires access to your screen information in order to generate the image shown on the DisplayLink connected displays, and permission to access your screen information is requested during the application’s installation.
Once this permission has been granted, whenever the DisplayLink Manager Application is running you will see a notification within the Apple Menu bar that the DisplayLink Manager Application is capturing your screen. This is both normal and expected behavior.
To be clear, no information is being recorded or stored by the DisplayLink Manager Application. DisplayLink (the separate company that develops the technology and the application software) speak to this in more detail here → LINK