Evidence of salvation is an epistle in itself. The salvation of the Corinthians was in Paul’s heart and in the hearts of those who were with him, for he was always thinking about it.
What means this, "you are?" 'Did we need to be commended to others, we should have produced you before them instead of an epistle.' And this he said in the former Epistle. "For the seal of mine Apostleship are you." [1 Corinthians 9:2] But he does not here say it in this manner, but in irony so as to make his question, "Do we need epistles of commendation?" more cutting. And in allusion to the false apostles, he added, "as do some, [epistles of commendation] to you, or letters of commendation from you" to others. Then because what he had said was severe, he softens it by adding, You are our epistle, written in our hearts, known of all...
[AD 384] Ambrosiaster on 2 Corinthians 3:2