If you know the order of the cards and can determine the “4th card” then I would just keep the flop and declare that 4th card as the exposed burn card for the turn.
Imo, ^that^ is the most logical and quickest way to resolve it. But unfortunately, it's not what the rule books state:
TDA:
39: Four-Card Flops and Premature Cards
If the flop has 4 rather than 3 cards, exposed or not, the floor will be called. The dealer then scrambles the 4 cards face down, the floor randomly selects one as the next burn card and the other 3 are the flop.
RROP:
Section 5: Hold'em
3. If the flop contains too many cards, it must be redealt. (This applies even if it were possible to know which card was the extra one.)
7, If the flop needs to be redealt for any reason, the boardcards are mixed with the remainder of the deck. The burncard remains on the table. After shuffling, the dealer cuts the deck and deals a new flop without burning a card.
Fwiw, I never really cared for the RROP rule, especially if the extra card was known/identified (it's merely the burn card for the turn). I dislike it mostly because it doesn't attempt to accurately re-create the intended flop, plus it essentially treats all of the initial flop cards (if exposed) as extra information available to all players, even though it might benefit some more than others.
The latest TDA rule is an improvement imo, and is written to cover all scenarios of a four-card flop (known order or not, exposed or not, etc.) and treat them all in exactly the same way. Interesting that they don't address flops containing more than four cards.
