One of my old bikes' exhaust was packed with fibreglas of something. The oil might saturate and hang on to the woolly stuff, but cause no harm.
When I put my bike away in the fall, I fill the tank with this oily treatment which goes through the exhaust as a vapour. My 250F has small holes where the stuff puffs out under the bike, so I know the pipes are getting "oiled" for the winter.
I don't know that the F has glas packing.
and my bike says she's envious of your bikes winter quarters.