The gemara says that according to the opinion that a metzorah is assumed to be a sinner because there are 7 aveiros for which tzara'as comes, the goat brought on YK could potentially be to forgive for those aveiros. The gemara answers - התם נגעיה דאכפר ליה וקרבן לאישתרויי בקהל, and rashi explains that the pain of the tzara'as is how he receives his atonement, so the korban is only to permit him back into the camp. The gemara seems to understand that the suffering of the actual tzara'as (which actually hurts as the gemara darshens - וטמא טמא יקרא, שמודיעו צערו לרבים ורבים מבקשים עליו רחמים), completely atones for whatever aveiros it came for, so that at the time of the korban he is no longer considered a sinner.
The Steipler (Birchas Peretz) asks that in the mishna Shekalim (5:3) it says that there were 4 tickets in the mikdash which one would purchase and redeem for the amount they needed for different korbanos. The ticket of the metzorah was labeled "sinner" - חוטא, and the bartenura explains based on the gemara in erchin that says that the aveiros for which tzara'as comes. But, based on our gemara which holds that he receives atonement from the pain of the tzara'as, why would it say "sinner" on the ticket at the time when he brings the korban?
The Steipler answers that even according to the opinion who holds that aveiros for which one already received atonement on YK he doesn't repeat next YK, would still hold of the concept - וחטאתי נגדי תמיד. When one did an aveira, even after receiving full atonement, it is necessary to realize that he had transgressed the aveira and received forgiveness, rather than being as if it were never violated. The rationale is that by realizing he did it in the past, he will have an awareness to avoid it in the future. It is for this reason that the metzorah is reminded even at the time of the korban, for which he was already forgiven, that he WAS a sinner.
I would like to suggest a slightly different p'shat. When one does an aveira they can receive atonement from the transgression with teshuva (and sometimes suffering), but there are certainly realities and consequences that don't go away so quickly. When one does an aveira that brings about tzara'as, he receives atonement from the pain of the ne'gah, but the halachic consequences such as being sent outside the camp are not removed with teshuva. Although the metzorah received full atonement through the suffering of the tzara'as, he is reminded at the time that he brings his korban that the reality and consequence of the aveira was being thrown out of the camp, and only now will he be permitted back it. It reminds a sinner that there is more to the sin than just atonement - he has to fix whatever consequences resulted from his sin.