I know you need the car, so that's a given. But have they indicated why you need the check valve replaced? If it's because of any debris, particularly metallic debris that might come from the pump, if it were me I'd do what I had to and turn the car in ASAP, with the absolute minimum of use. A $550 bill looks a lot better than one ten times bigger. Not a good recommendation, I know, but that's what I think. As for the charge for the repair, I'd have no clue.
This sounds like good news (at least as good as it can be, under the circumstances).
The warranty does not start until you get the fixI was under the understanding that VW has agreed to extend the warranty to cover all engine, emissions, and transmission repairs, including the HPFP and injectors, as part of the settlement.
I don't know if it only applies to TDI vehicles AFTER they have had the 'compliance fix', of if they will extend it to those with problems before the fix due to their non-compliance.......
Its worth an ask....
Gary