Yes, the point of the GP comment is exactly this, if Bentham becomes an agent that goes for C, he also explicitly discourages the mugger from being an agent that would cut off their fingers for a couple of bucks.
Notice that what Bentham is altering is their strategy and not their utility. If they could spend 10 dollars to treat gangrene and save the fingers, they would do it. It's not clear many other morality systems would be as insistent on this as utilitarianism, because practitioners of other moralities curiously form epicycles defending why the status quo is fine anyway, how dare you imply I'm worse at morality.
Notice that what Bentham is altering is their strategy and not their utility. If they could spend 10 dollars to treat gangrene and save the fingers, they would do it. It's not clear many other morality systems would be as insistent on this as utilitarianism, because practitioners of other moralities curiously form epicycles defending why the status quo is fine anyway, how dare you imply I'm worse at morality.
Edit: Slight wording change for clarity