Don't scrub the thing, tissue and lens cleaner or ammonia solution.
Don't press the tissue flat, make a ball or wad about 3/16-1/4" and use a circular motion.
It's going to take several applications, just take it easy.
Older lenses have much softer internal coatings than newer, careful anyhow.
BTW I've successfully removed inner coatings myself. intentionally(cough), right
I was thinking of using one of those cloths for glasses. I heard that using tissue paper can end up creasing because of some stiff fibers or something...