In the tradition under review...
In the tradition under review, it is stated that even if a person had intentionally done something and then comes and wishes to place himself under the covering of your forgiveness, you must show your greatness of character and not let your ego get the best of you. In addition, one must even accept the apology of a liar - of course there are certain times and circumstances which are an exception to this rule and are separate from this discussion (which we will not discuss).
However if one was not to accept the apology of another person, then slowly the veils of inhibition and shame would be removed from all people! If someone comes and apologizes and one was to reply, “No, you are lying, you are not sorry for what you did” then that person may actually begin to act even worse and may reply, “It is my heart which wanted me to lie (to you and to try and fool you that I was sorry…)” At this point, what road would you take to stop this person's obstinacy?
Therefore, in order for us to earn the pardon of Allah (SwT), we must be ready to forgive at least one sin from another person and accept their apology. In addition, in the Du’a of the month of Rajab we say: يُعْطِي مَنْ سَئَلَ… “You give to the person who asks You…” However in addition to this, we see that later on in this Du’a, Allah (SwT) not only gives to those who ask Him, but also those who have not recognized Allah (SwT) for their entire lifetime!
These people are still covered and included in the mercy of Allah (SwT) (see the rest of the Du’a of the Month of Rajab). It is Allah's i mercy that is such an All-Encompassing Mercy that it does not deprive a single person, not even the one who do not ask Him for a single thing - He even gives to them!
The word used in the end of the tradition under review is “منتصل” which means a person who wishes to exonerate or absolve himself of something which he has done - meaning that he wishes to apologize for his actions.