Problem: The file icons displayed in WebDrive include a small "x" in the lower left corner. This only shows up for files in the WebDrive mapping.
Solution: The icon overlay is a result of the setting "Disable Explorer icon handler to prevent file download" in Site Properties --> Basic File Settings. The overlay is associated with the offline attribute, which Windows uses to denote the fact that it can't pull down the icon information. This setting is enabled in WebDrive by default in order to avoid uninitiated downloads of files simply to extract the icon information. Disabling this setting removes the icon overlay, but may result in increased/unintended file downloads.