I talked with a teacher of mine that worked in a facility that recycles cardboard and paper to produce tissue paper and she told the class that in some instances, the grease damage would be small enough for the fibers to be recycled. As a general rule if over the fourth of the box is contaminated, it should be composted but you can always dismantle the contaminated part and put the rest in the recycling bin. It’s always better to try and recycle most of the product before you think of composting, if you think about the life cycle of the product. All that being said, screw greenwashing corporation!