If they have to get involved, IMO, they should send SpaceX the bill.
It's a fixed cost contract, while SpaceX might push back on accepting the bill in the first place, they are unlikely to be able to redirect it to NASA if they choose to accept the bill.
Of course, I would expect to see this cost reflected in all future contracts they and anyone else signs with NASA.
Most of the time, letting your kids play in a Superfund site won’t lead to a bad outcome. That doesn’t make it sensible.
Hydrazine didn’t leak this time. That’s good. But it’s a stupid dice to roll.
Government agencies can only impose fees and charges on private entities where those are authorised (directly or indirectly) by legislation. And agencies have far greater discretion to make contracts in which they are the customer than those in which they are the vendor. The later kind of contracts generally need approval at a far more senior level than the former (in some cases even requiring approval by the legislature).