You can put your EMPTY pizza box in the recycling bin. Grease is okay. This includes pizza boxes (with the exception of frozen pizza boxes) made out of cardboard or box board (think cereal box) as long as they are empty. Helpful suggestion: fold the box inside-out before you put it in the recycling. This will make sure that the box is completely empty so there are no surprises at the sorting facility.
Liners and pizza savers (pizza tables) go in the trash. Leftover food should be composted or put in the trash.