Since Delta does not fly its own metal out of ITO, then will need to fly HA to either OGG/HNL and connect from there on DL metal. Since you mentioned Virgin, this is where I get confused, because there is no way that I know of to get to the mainland from the islands on Virgin (and the other poster is correct, they are not a partner). Did you book a Virgin Atlantic codeshare on DL metal??

As someone who travels quite frequently to the islands, I find it cheaper, and easier to just pay out my own pocket for ITO-OGG/HNL on HA and then fly DL metal, or rent the car and drive the 2 hours to KOA and fly DL metal from there.

I do believe Alaska Airlines flies to SEA from ITO so that may be an options as well.