If player pulls card out of his hand and then puts it back in his hand, and opponents have seen the card, must player play that card?
The relevant rule is Law 45 (C) from the Laws of Duplicate Bridge (2017)
LAW 45 - CARD PLAYED
C. Card Deemed to be Played
A defender’s card held so that it is possible for his partner to see its face is deemed played to the current trick (if the defender has already made a legal play to the current trick, see Law 45E).
Declarer is deemed to have played a card from his hand if it is: (a) held face up, touching or nearly touching the table; or (b) maintained in such a position as to indicate that it has been played.
A card in the dummy is played if it has been deliberately touched by declarer except for the purpose either of arranging dummy’s cards, or of reaching a card above or below the card or cards touched.
(a) A card is played if a player names or otherwise designates it as the card he proposes to play (but see Law 47).
(b) Declarer may correct an unintended designation of a card from dummy until he next plays a card from either his own hand or from dummy. A change of designation may be allowed after a slip of the tongue, but not after a loss of concentration or a reconsideration of action. If an opponent has, in turn, played a card that was legal before the change in designation, that opponent may withdraw the card so played, return it to his hand, and substitute another (see Laws 47D and 16C1).
So to answer your question: No, a Defender's card is not played simply because an opponent (Declarer) can see which card it is; rather it is played if it is held so that the Defender's partner can identify it,
Further clarification through Minutes of the W.B.F. Laws Committee, where necessary, are available here.