whats the ruling?

[Brettski]

Take the river card back, complete the action on the turn betting round, reshuffle the card in with the stub and re-deal the river without burning a card. This is the ruling at Crown in Melbourne, Australia.

In poker it's important to keep the cards in sequence as best as one can. Given the fact that the third burn card sticking out from underneath the pot is "in sequence", it should stay there.

Rules regarding prematurely exposed board cards can vary quite a bit from cardroom to cardroom though.