The controversy led to the mother of a grooming gangs survivor, known as Taylor, saying she no longer had confidence in Constance.
Opposition MSPs triggered a vote of no confidence against the justice secretary in December.
The justice secretary survived the vote but shortly before Christmas the Scottish government’s independent advisers confirmed that they would investigate her comments.
Constance made the remarks about Prof Jay when she opposed a Conservative amendment to a victims bill, which called for an inquiry into grooming gangs.
Emails released by the government later showed Prof Jay clarified that she made the comment quoted by Constance “in the context of the England and Wales Public Inquiry on Child Sexual Abuse,” which she chaired.
Prof Jay wrote: “It had nothing to do with [the Conservative] amendment, or the position in Scotland, as could be interpreted from your statement.”
She urged the government to clarify her position.
Constance apologised to Prof Jay at a meeting of Holyrood’s education committee.
She said she made an initial apology in a “personal” telephone conversation with the academic.
However, the committee heard no government officials were present on the call – sparking further accusations of a ministerial code breach.
After the independent advisers announced their investigation, Constance told BBC Scotland News that the row could have been “handled better” but that she had acted in “good faith”.