The Inn Sign Society has a special section on its website about cats. It says that the first recorded mention of a Cheshire Cat was in 1770, and a pub called The Cheshire Cat in Christleton, near Chester, commemorates this.

Carroll spent his early life in Cheshire, but it's not known if he ever visited this pub. It dates from 1801, which is thirty-one years before his birth; so it is by no means impossible.

He would probably have liked the Inn Sign Society: he was all for saving traditional things.