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The Mishna that opens the twelfth perek of Massekhet Menaḥot deals with questions of redeeming other sanctified items. We learn that meal offerings and libations can be redeemed so long as they were not placed in a keli sharet – a Temple vessel that would give them full sanctity.
Once they were placed in a keli sharet, however, they cannot be redeemed even if they became ritually defiled and cannot be brought as an offering. Similarly, sacrifices brought from fowl, or wood sanctified for use on the altar or frankincense or a keli sharet that became ritually defiled and cannot be brought or used in the Temple, cannot be redeemed.
These items will have to be destroyed, since the concept of redemption appears in the Torah only with regard to animal sacrifices that cannot be brought on the altar.
The Gemara on our daf teaches that the restriction on redeeming the last three examples – wood, frankincense and Temple vessels – is Rabbinic in origin, and that on a Biblical level they can be redeemed, even if they did not become defiled and were fully usable.