Law 40C3a said:
Unless permitted by the regulating Authority, a player is not entitled during the auction and play periods to any aids to his memory, calculation or technique.
Law 17A said:
The auction period on a deal begins for a side when either partner withdraws his cards from the board.
Definitions said:
Auction: 1) the process of determining the contract by means of successive calls. It begins when the first call is made.
Once a player (or his partner) takes his hand out of the board, the auction period has begun, and he is not entitled to any aids, etc. The only thing "Secretary Birdish" I can see here is the assumption (which may well be correct) that reminding one's partner of a partnership agreement during this time violates Law 40C3a.
I think that it's true that such discussion rarely draws objection from the other side, unless they've already finished counting their cards and are ready to proceed (and, probably, are concerned about being behind). I also think that if someone does object, and calls the TD, the TD has to deal with it fairly and IAW the laws. On the gripping hand, I suspect that far more often when there's an objection, the pair shuts up and they just get on with the game.

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