The Remote Buddy menu is transparent for mouse clicks for technical reasons: actions that you trigger using the menu might need to click on parts of your screen (that may be covered by Remote Buddy's menu) to perform their task. If Remote Buddy's menu reacted to mouse clicks and not just let them through to the underlying windows, you'd get undefined behavior in these cases.

There is an easy way to dismiss the Remote Buddy menu without the remote, though: just click on the Remote Buddy icon in the menu bar and the menu will fade out.

Best regards, 
Felix Schwarz