The decision to shred and reprint 18,000 copies at a cost of £4,850 was made without Delaney's knowledge.
Delaney wrote his column prior to the revelation he had accepted a payment of £3.62m from Fifa on behalf of the FAI.
He said the payment was to stave off a threatened lawsuit against Fifa.
The threat came after match officials missed a handball by Thierry Henry as the France striker set up William Gallas's crucial goal in a World Cup qualifying play-off game against Ireland in Paris in 2009.
An FAI spokesman said: "John Delaney was entirely unaware of this change to the programme.
"He had already signed off on it and it was approved for printing.
"The decision to delete his comments where they related to Fifa was an editorial one that was taken by the communications team."
After news of the payment from Fifa, a group of supporters have paid for a banner to be flown over the Aviva Stadium in protest an hour before Saturday game in Dublin.
Fifa is facing two criminal investigations into alleged corruption, while long-serving president Sepp Blatter is to resign following reports he is under investigation in the United States.