There is a difference between the ideas of apology and revelation or confession. When we in the west read in the suttas about some person recognizing his mistake, we should not be thinking he is apologizing. The idea is that by confessing ones understanding that one has made a mistake and that one understands the nature of that mistake one has made the details conscious. Conscious of the error and the corrective measures needed to prevent its repetition, one is then in a position to take those corrective measures. It is the making conscious that is the important thing.
Apology is asking for forgiveness, not necessarily stating that there will be any effort to reform.
In both cases there is the idea that once an error is sincerely confessed, or a wish for forgiveness expressed in an apology and the other person does not acknowledge the confession or forgive the transgressor, the bad kamma of the deed passes over from the one who is confessing or apologizing to the one confessed to or apologized to. It is beyond my scope to comment on the reality of this belief.
In the case of the apology, going by the Christian practice, there is no requirement that the transgressor understand his error, and one is supposed to forgive, '“seventy times seven times” (490) (Matthew 18:22), a number that symbolizes boundlessness. ... '
In the case of the confession the transgressor must express an understanding of the error and corrective measure before it is necessary to acknowledge it. In this case (and we do not have an example in the suttas so this is just me making up what seems to be a logical response), the polite thing to do would be to explain exactly what was needed before the error could be acknowledged. A diplomatic construction of the statement: "You have not understood your error and consequently I am unable to acknowledge it for you." With perhaps an explanation such as made above to point to what is needed to be done by the transgressor in order to turn this exercise into something helpful to the goal, i.e., change of behavior.
Since the distinction between confession and apology is not likely to be known by most persons in the west, a further act of kindness when faced with an apology that looks to be a sincere effort at change for the better would be to explain this distinction and by that give the person an opportunity to change the apology into a confession.