I am not really sure they attached this to your house right at all. I would need to see a picture.
The board that is against your house is the ledger. This runs parallel to your house you should see it bolted in. This would be load bearing (along with your posts) and is bolted into floor joists - which are not 2x4s.
Now you can run joists that attach to your house perpendicular to 2x4s. Meaning that You would have a couple of simple attachments that space/attach the deck to your house but this is not usually load bearing - load sits on the concrete posts. I don't think this is what you are talking about.
Back to the ledger... There should be flashing over the ledger (and under above siding) to prevent water from entering your house. Also your siding should be tight to deck and caulked. See the flashing picture below.
They can pull the interior deck boards and add the flashing - make sure they do the edges too because taking down the railings on each side will be some work for them. I am not really sure about the quality of the install if they missed this though. I am not a "deck" expert and this is just common sense. Also you saying the ledger is attached to 2x4s makes me wonder. Not saying that your deck was installed wrong other than the flashing but pictures and more info would help.
Edit - There is a way to add flashing when you forgot. See picture below for an example.
You see how this has to be notched into the joists. Because the flashing is usually under the joists. Personally I would call the city and make sure this doesn't pass inspection. Usually there is flashing completely under the ledger, above the ledger, under the joists attached to the ledger... At first I was thinking about retrofitting flashing but thinking about it more makes me think this is a tear down. You paid for this deck to be done right and no matter what - unless they pretty much take everything down minus posts - it isn't really right.