No ours doesn't have a cover, just a little dial at the bottom, which catches the flap on one, the other, both or no sides.

Yes, We'll have to lock it totally.

Shame though, it was handy to put the flap on 'in only' and all cats entering the house would stay in. Now we'll have to call/ catch all cats and lock the flap down completely... cats.

(I still think he is one clever cat, even if it causes problems.)