Even without the tomato sauce and grease, unsorted paper is pretty useless for recycling. They want each type of paper separated. At pennies a pound, sorted you can't afford to sort it after it gets mixed. That is why you see "cardboard only" dumpsters behind places that handle a lot of boxes and the recycler might reject the whole dumpster if he sees anything else in there. It was the same when we were recycling computer paper. Anything that wasn't white bond paper was rejected and the guy would reject the whole load if he saw some of the "recycled" paper in there.
These days we should only be putting metal, #1 and #2 plastic in the recycle. Everything else should be burned for electricity or landfilled.
Landfill is pretty cheap as soon as you get away from the Acela corridor.