There is nothing wrong with placing left-over pizza in the fridge in the cardboard box that the pizza came in--especially if you will be eating the rest of it the next day. The reasons for doing so are the following:
1.) The cardboard box will be out of the fridge and in the trash within a day, anyway.
2.) The cardboard box is so much easier to use rather than pulling out a new dish and wrapping it up.
3.) When heating your pizza the next day in the oven, the cardboard box provides the perfect cover for the pizza.
So please, leave the cardboard box alone. It is one of man's best friends.