So how can one explain the current practice of destroying the terumah or burning it? Is this a mistaken custom? Or since, according to what you wrote, in any case this is only a very small gift (one grain of wheat, and even less than a perutah’s worth), presumably the kohen waives it? Or is there no theft involved in less than a perutah’s worth?

I think this is a custom that developed so that kohanim (or others) would not come to use the terumah in some way other than burning it.
Indeed, it is less than a perutah’s worth, and the presumption is that a Jew waives such a claim.
But as I explained, at least according to Maimonides and those who follow him, the kohen does not need to waive it at all, because it does not really belong to him. There is an obligation to separate, not to give (the giving is from Heaven’s table). And even if there is an obligation to give, that is an obligation on the giver and not a right of the kohen.

Following up on the issue of the obligation to give terumah according to Maimonides (that there is no obligation): how does this fit with the Talmud in Kiddushin 6b: “Rava said: Here is a maneh on condition that you return it to me—in a sale, he has not acquired; with a woman, she is not betrothed; in redemption of the firstborn, his son is not redeemed; with terumah, he has fulfilled the obligation of giving, though it is forbidden to do so, because he appears like a kohen assisting at the threshing floor.”
Seemingly, it sounds like there is a concept of fulfilling an obligation by giving terumah to a kohen.

Perhaps the intent is that rabbinically this does not release the produce from its tevel status, and not that it concerns fulfilling a commandment-obligation. That is also what seems from the wording of the Talmud, that it is forbidden to do so because he appears like a kohen assisting. In other words, the tevel is corrected, but rabbinically it is forbidden to do this.
By the way, this is not ruled that way in practice, and therefore Rav Ashi indeed says, “In all of them he acquires,” and the law follows him. If so, even if you are right, one could say that according to Maimonides this is only Rava’s opinion, and Rav Ashi disagrees.

I thought perhaps one could answer that with regard to the declaration over the tithes, there is an obligation to give terumah to a kohen; and one who gives terumah to a kohen on condition that it be returned has fulfilled the obligation of giving, and therefore no longer has an obligation to remove the terumah in the third and sixth years.

And if he has not fulfilled it? Is there really even an initial thought that he must remove what is in the kohen’s possession?

If he has not fulfilled it, then he has to give the terumah to a kohen before Passover of the third and sixth years, and by doing so he removes it from his house, and then he can declare, “I have cleared out the sacred portion from the house.” Why would he need to remove what is in the kohen’s possession? It is not his.

So apparently I did not understand your suggestion. We are discussing a case where the terumah was already given to the kohen on condition that it be returned. At the time of removal it is in the kohen’s possession. So what exactly would he remove?

Now I understand what you meant from the start. The Talmud raises a doubt regarding a gift on condition that it be returned—whether it is considered a giving or not. I think both sides of the doubt refer to a situation where the kohen returned the terumah to the Israelite (that is, at the time of removal it is in the Israelite’s possession), and one side of the doubt says that even though the kohen returned the terumah to the Israelite, the Israelite has no obligation of removal; and the other side says that although there was a giving to the kohen (and a return), there is still an obligation of removal, because this was not a real giving to the kohen.

That also seems to be Rashi’s meaning there: “He fulfilled the giving”—and he may sell it to kohanim, and the money is his; and later the Gemara challenges this from either side.

But clearly, even after it is returned, it is still terumah (it does not suddenly become ordinary produce), so in any case in the end it must be handed over to a kohen. Therefore it seems logically that this too should require removal.

Beyond that, it is fairly clear that even according to Maimonides there is an obligation to hand terumah over to a kohen; it is just that there is no fulfillment of a commandment in doing so. From the law of recognized priestly recipients as well, it seems that terumah is property of the kohanim (the priestly tribe. The benefit of choosing the recipient belongs to the owner).

So perhaps according to Maimonides, when the Talmud says “he fulfilled the giving,” it means he fulfilled the obligation to give—an obligation that is not itself a commandment—and now he no longer even has that obligation?

Possible, but on the face of it that is not so likely, because the obligation to give derives from the very fact that I have terumah in my possession. But as stated, this is only an initial thought that is rejected, so perhaps Maimonides too would agree that this was based on the assumption that there is a commandment of giving, but in the conclusion that is rejected.

Now I was thinking that maybe the meaning of the words “he fulfilled the giving” is that there is an obligation for the transfer to be done as a gift and not by way of sale. Not that there is an obligation to give, but that if the Israelite wants to rid himself of his terumot, this must be done by way of giving and not by way of purchase and sale. One who gives his terumot to a kohen in exchange for payment has not fulfilled “giving,” because this is not the manner of giving. Just as with Sabbatical-year produce there is no commandment to use it, but if one does use it, the use must be by way of eating and not by way of commerce, and one who trades in Sabbatical-year produce has not fulfilled the obligation of “for eating” (or the obligation of eating).
And similarly it appears in Bava Metzia 11b: “Priestly gifts—the Torah wrote ‘giving’ regarding them; barter is a manner of buying and selling.”

Check there again and you will see that the Talmud’s intent is different. Barter comes to exclude an ordinary sale for money or acquisition through land, which are indeed considered giving. It is not coming to require specifically a free gift. Barter is not giving at all, but an ordinary sale is.

Okay, but one can still explain it similarly: that one who gives his terumot to a kohen as a gift on condition that it be returned, this resembles the way of trade and barter rather than the way of giving (not that giving is defined as absence of payment, but as a mode that is not barter), and therefore there is an initial thought that he has not fulfilled the giving. The Talmud teaches us that even so—he has fulfilled it (because it is not entirely barter).

Also, from the continuation of the passage in Kiddushin one can see that a gift on condition that it be returned is regarded as somewhat like barter: “Rav Ashi said: In all of them he acquires, except for a woman, because a woman is not acquired through barter.” And Rashi on the Gemara in Bava Metzia also seems to indicate that it is forbidden to give terumah by way of barter (a commercial transaction): “The Torah wrote ‘giving’ regarding them”—as it is written (Deuteronomy 26), “And you shall give it to the levi”—this is first tithe; “to the stranger, the orphan, and the widow”—this is the poor tithe. Therefore it is forbidden to transfer them by means of a kerchief, because that is the manner of a commercial transaction, where this one gives him his vessel in exchange for them, and it appears as if he is selling them to him.

But now it is difficult why the law of acquiring a woman by a gift on condition that it be returned is different from the law of terumah. For if a gift on condition that it be returned counts as barter, then terumah too should be forbidden to be given that way; and if it is not barter, then a woman too should be acquired by it. So perhaps one has to say that with a woman even resemblance to barter is forbidden, whereas for terumah it is enough that it not be actual barter, and resemblance is permitted.

A woman through barter is the topic in Kiddushin 3a. See there the dispute between Rashi and Tosafot, and also the Ritva there (whether this is rabbinic or Torah-level). I once explained that this is essential, because barter creates ownership over a physical entity (body for body. That is why coins and produce do not work for barter, because they have no “body”), and that does not exist with a woman.

Regarding what you wrote above, that perhaps according to Maimonides Rav Ashi disagrees with Rava about the commandment of giving, I saw that Maimonides rules there explicitly in Laws of Terumot, chapter 12, halakhah 19:
“One who gave terumah to a kohen on condition that it be returned has fulfilled the giving, and it is forbidden to do so because he is found to be like one assisting in the threshing floor.”
That is, it seems that according to Maimonides too, Rav Ashi agrees with Rava that one must fulfill the giving.

It is possible that he rules like Rav Ashi דווקא because there is no need for giving as a commandment. Precisely for that reason one has fulfilled the obligation.