SSH expects the escape sequence (tilde) to be the first character on a new line; since backspace is sent as a character, you can't just backspace over something you've started typing and then press tilde to have it recognized.

Technically, you don't have to press enter if you've not typed anything (try it in a new SSH session - as soon as you are logged in, type ~? to get the SSH help output), but since the comment was about doing this during an active session without ending it, I figured noting that pressing enter first to be sure you're on a new line wouldn't hurt