Sounds like epoxy, and the heat it would take to loosen the epoxy will ruin your stock finish. Epoxies that are bonded to things unaffected by heat, like steel, can be removed with heat. On a wood rifle stock? I surely wouldn't.
Luthiers use hide glue which can be removed with heat like a heat gun or maybe a hair dryer. Whoever put that pad on there wouldn't be using animal hide glue - it's specialized in its application.
Try what xjsdvr is recommending - ice or dry ice on a towel. Then, with a very sharp (woodworking!) chisel and extreme care, you might be able to pop it off a little at a time.
Anyway, sure sounds like epoxy. DON'T sand it. Better, if you don't have razor sharp wood chisels and experience using them, take it to a woodworker or cabinet shop. They'll shave it off, THEN you can sand it. You'll have to refinish it sure sounds like.
EDITED TO ADD: Well, almost certainly it isn't "hot glue" unless you were very tentative with your hair dryer heat. If you suspect it might be, you might try heating a tad more aggressively a second time. Caution still, as you know, because even though it looks like you'll have to refinish, you just don't need the mess. See, imagine you get the glue off, but it isn't shaved right down flush with the stock...right down flush! What you have left is a slight running mound - imagine a worm underneath the surface of your stock with a portion of his back exposed. When you try to sand that, even with a block, you will over-sand the other areas of the stock because the wood will yield well before the glue does.