I've seen this happen before - I think it happens as the clutch plate friction material absorbs moisture and then rusts / sticks to the flywheel face. You dont want to be putting any grease or oil on there as when you finally use the car - the clutch willl slip. Not sure if there are any products you can use on there though.
My Kubota tractor has a block of wood that comes with the tractor new. It's purpose is to hold the clutch pedal down while in storage for a period of time. The block of wood is positioned between the floorboard and the clutch arm. This keeps the disc from touching the flywheel. This could be used with maybe a brick or something else to keep the clutch from freezing onto the flywheel. Just an idea that would be easier than removing the trans.