The simplest strategy to optimizing an overlay for desktop and mobile is to create two separate overlays: one that is visible to only desktop users, and one that is visible to only mobile users. Then build out the overlay settings, CSS code, and HTML code so the overlay appears best on a given device.
This configuration change is done under DEVICES in the TARGETING tab in the Overlay Builder.
Select the Desktop only option and build the overlay to be best viewed on the desktop. Select the Mobile only option and build the overlay so it is best optimized for mobile devices.