Here's a fix that worked for me. You'll need to have Apple's developer tools installed, though.
Open the Finder to /Library/Application Support/Logitech. Find Logitech Control Center Daemon, right-click it, and choose Show Package Contents. Go into Contents/Resources and open NotificationSquareWindow.nib.
When Interface Builder appears, double-click View. Next, click in a blank area of the View window that comes up (it is labeled with an A for application, Title, and Information). Then choose Tools->Show Inspector. The Inspector window should be labeled "AZNotificationWindowView". If not, you've got one of the user interface elements selected, so be sure to select a blank area of the window.
From the drop-down menu at the top of the Inspector, choose Attributes, select Hidden, and then choose File->Save.
Hopefully, this hack will work for you, too.
