When Eric sees the principal is on TV taking back what he said about Billy he throws the stapler. You can see the stapler on the floor before you hear it hit his secretary in the head.
It is a remote because he was watching TV and got disgusted by Max's reprisal. Director's call the remote visible on the floor "Sight Projection". It is there to show you she got hit with the remote, otherwise it would be, as they call it, an "empty" scene.