The contract was to replace an antiquated HVAC and duct work. Since the registers are a standard size, would this connection also be a standard pre-fabricated part? What is that last connection called?
I believe it's called a "boot", and yes, they're generally pre-fabricated.
However, if the existing ones are in good shape, they shouldn't need replacing. If they're damaged, then the reasonableness depends on what your contract says.