Is one required to repeat the prayer if one becomes certain of the impurity of one's clothes after the prayer, when one's previous doubt about their impurity before the prayer was, in fact, true?

You are correct; doubt about the impurity of a garment does not make it impure unless certainty of that is achieved. If you did not ascertain the impurity of your garment until after the prayer, then, according to the more correct of the two scholarly opinions, you do not need to repeat the prayer.