When you get a chance, spray them to soak them as already suggested and wear protection like I mentioned. Better safe than sorry when it comes to disturbing it, even though you won't actually be breaking the material itself by removing the doors.
Does it make more sense to not disturb them until the last minute? Or remove them now, leave them in back yard? The latter option bothers me. More risk of damage?
When you get a chance, spray them to soak them as already suggested and wear protection like I mentioned. Better safe than sorry when it comes to disturbing it, even though you won't actually be breaking the material itself by removing the doors.