If the insulation
has been glued down with construction cement it could be cut away with a fairly fine toothed wallboard
saw, then the construction glue could be carefully chiseled out with a chisel and a small mallet.
The above links lead to some safety
requirements for small saws that are good advice.
I have been known to use a 10" piece of 3"x1.5" pine instead of a mallet when desperate. Light taps are all that is needed.
Keeping the area nice and clean with a wet and dry vacuum cleaner is a decided plus.