Albert Barnes Commentary 2 Corinthians 13:6

"But I hope that ye shall know that we are not reprobate." — 2 Corinthians 13:6 (ASV)

But I trust, etc. The sense of this verse is, "Whatever may be the result of your examination of yourselves, I trust (Greek, I hope) you will not find us false and to be rejected; that is, I trust you will find in me evidence that I am commissioned by the Lord Jesus to be his apostle." The idea is that they would find, when he was among them, that he was endowed with all the qualifications necessary to establish a claim to the apostolic office.

"Reprobates" in this context means "disapproved."