Dishes, crockery, or utensils that have become forbidden to use, whether on account of having absorbed the taste of meat and milk or on account of having absorbed the taste of non-kosher meat, may not be koshered on Yom Tov. The specifics of the absorption are immaterial; whether the absorption involved liquids (in which case the koshering process involves hagala) or was through fire (as in the case of a baking pan or skewer, in which case the koshering process requires heavy libun), one may not do the koshering. This is because making the item usable looks too much like repairing it (SA and Rema 509:5). True, if the utensil could not have been koshered before Yom Tov, and it is needed, it may be koshered on Yom Tov following the laws for makhshirei okhel nefesh. However, this law should not be taught publicly, because of a concern that some of the audience will end up being lenient in other matters, where there is no room for leniency (MB 509:24, 26).
As is known, crockery and cutlery that a Jew acquires from a non-Jew require immersion in a mikveh. Until they have been immersed, they may not be used. Rishonim disagree as to whether a utensil may be immersed on Shabbat and Yom Tov. Some forbid doing so, because it looks like “repairing” the item (Rosh). Others permit it, as this is not a full repair, because be-di’avad, if the utensil was used prior to immersion, the food in it is not prohibited (Rif). In practice, if a trustworthy non-Jew is available, it is proper to gift him with the utensil and then borrow it from him, because as long as an item belongs to a non-Jew, it does not require immersion (Peninei Halakha: Shabbat 22:6).
If no non-Jew is available, the disagreement remains unresolved. However, on Yom Tov, even those who are stringent agree that technically, as long as one could not have immersed the utensil before Yom Tov, he may immerse it on Yom Tov. For we have seen that it is permitted to repair makhshirei okhel nefesh on Yom Tov. In practice, though, according to those who prohibit immersing utensils on Shabbat, a rabbi should not tell an inquirer differently on Yom Tov, out of concern that he will not understand the reasoning behind the permit and will end up mistakenly permitting other cases as well (MA; Eliya Rabba; MB 509:30).