Hi Hr:
When you say "mucks the flop together with the deck", do you mean the muck with everyone else's folded cards are still separate, or are both the flop and the muck mixed in with the deck? What about the burn cards?
If any of the mucked cards and/or burned cards are still separate, keep them separate.
Then, let D complete his action. Obviously, if he folds, then there is no issue.
If D calls, or if D raises and C calls, etc., the general approach would be that you would remove the proper flop cards from the pile that it is in. ( I am assuming that the top of what would have been the proper deck is no longer intact, because if it was, you would try to use that part when salvageable, in order to deal the turn and the river ).
After putting out the original flop, you would re-shuffle the mixed-up deck that you have, cut, burn, and continue to deal the turn and river as normal.
If the muck was never mixed in, the reshuffle is not a huge deal, since the deal is still random, and no folded cards will come out on the turn or river. If the muck was mixed in, of course, the situation is not ideal because one of the folded cards could, in theory, appear on the new board, but this is making the best of a bad situation. At least, neither D nor E knows the identities of the folded cards, so they will be equally affected should a folded card happen to appear on the board. Both players are equally disadvantaged, and there is no information imbalance.
However, you can see that the underlying principle is that you need to do whatever is necessary, given that action has begun, to see the hand through to completion. Ideally, we'd like to preserve as much of the original board as possible, but even when we can't, if neither player has any special knowledge of what cards may or may not be in the deck, there should be no serious issue with play continuing after a reshuffle.
Note that if the procedure were to automatically call for a misdeal, for example, there would be too much of an incentive for players to collude with dealers, and signal to the dealer when hands should be "accidentally" killed to trigger a refund of bets when it is clear that someone else is likely to win the hand. The incentive could be particularly high on a later street (e.g. Turn card is dealt, raising war ensures, both players all-in, and then deck becomes compromised for whatever reason). Once substantial action has begun, a misdeal cannot be called.
Hope this helps.
K-Lo