Kesef Asham and Kesef Chatas are for the Korban! How can they go to the Kohanim?
Rashi: The verse discusses [excess] money that was Hukdash for the Korban, that remains after it is bought.
Does the verse forbid bringing the money to Beis Hashem?
Rashi: It is not for Bedek ha'Bayis.
What will the Kohanim do with the money?
Rashi: It is for Kitz ha'Mizbe'ach (Olos Tzibur to offer when the Mizbe'ach is idle. The meat is burned on the Mizbe'ach, and Kohanim receive the skins. Yehoyada ha'Kohen expounded 1 , all that comes from extra money for Chatas and Asham, we buy Olos with it (Temurah 23b).
Radak: He expounds "Asham Hu Asham Asham la'Shem" (Vayikra 5:19). Malbim - it says also "ha'Asham Hu la'Kohen" (Vayikra 14:13). Since Kohanim receive the skins, both verses are fulfilled.