Interesting.
I'm certain that the missing wood is of a greater volume than a strip of construction paper. How would the paper stand up over time?
I have a gun that I've used for over 30 years with paper in it
It holds up real well
I learned this trick when I worked at GRRW
It can used to fill slight gaps in the butt plate or along the side of the tang
Put glue on the wood side and put the barrel back in until it dries
once dry you can file or sand it
the paper takes AF well and the finish hides it
very slight gaps can also be filled in by rubbing with beeswax
if you use a linseed oil/beeswax finish they blend right in
for really big gaps use a wood sliver