There are plenty of ways to look at such a windfall.
First of all ... how does the contractor ordinarily treat materials that he encounters? Does the insulation, wood fire blocking, soil, .... in short, everything he encounters ... become his? Are old materials, replaced fixtures, etc., his? In my world, that stuff all is the customers' property, for them to dispose of as they wish. If they let me recycle the scrap, well, that's nice ... but I never consider that I have such by right. If I end up making a dump run, I will typically add that to the bill - another indication that the removed stuff belongs to the customer.
Let's look at it from another view - the customers'. They are stuck with the property 'as is.' If they find oil or gold on it, they generally have the first rights to that wealth. If the place turns out to be a superfund site, they get stuck with the loss. Win or lose, it's their risk.
Then there is the matter of 'who owns the money.' Since it was identified on the wrappers, it is quite possible that the heirs of the original owner have a claim to is, as part of their estate.
Don't forget the government. First of all, the tax authorities will want their cut. I suspect that, had everyone split the money and kept quiet, they both would have done better than anyone will, after the government takes its' cut .... IF the government takes the position that the money is the proceeds of illegal activity of any sort, they may simply seize it ... with little recourse by anyone.
Finally, what if the contractor had quietly loaded it on his truck, and kept his mouth shut? The customer would have been far happier than they now are.
It's simply amazing how a little money can bring out the worst in people. It's "found money." No one expected such a windfall. Both parties ought to be generously offering the other as much as they want. Or, even, debating a worthy charity to receive part. After all, such generosity would cost them nothing ... whatever is left is still an unexpected windfall.
One thing is certain: everyone involved will suddenly find that they have all manner of friend! Business offers and charity pleas will rain down on them. Their phones will ring non-stop. They will find themselves echoing the words of author Alex Hailey (Roots): "Some days I wish it had never happened."