טובת הנאה לבעלים the benefit of discretion for the owners of the produce, i.e., benefit accrued from the option of giving teruma and tithes to any priest or Levite of their choosing.
כיצד ישראל שהפריש תרומה מכריו ומצאו ישראל אחר ואמר לו הא לך סלע זה ותנהו לבן בתי כהן מותר אם היה כהן לכהן אסור The baraita continues: How so? With regard to an Israelite who separated teruma from his pile of grain, and another Israelite found him and said to him: Take this sela coin for yourself and give the teruma and tithes to my daughter’s son who is a priest, it is permitted. But if it was a priest who gave the sela coin for the right to give the teruma and tithes to another priest, it is prohibited. Priests may not pay for the gifts that they receive.
ותנא מאי טעמא לא קאמר מתנות כהונה אמר לך תרומה דקדושת הגוף היא דכיון דלא מתחלא לא אתי למיטעי בה The Gemara asks: And according to the tanna of this baraita, what is the reason that he does not state that the owners also have the benefit of discretion with regard to the gifts of the priesthood, i.e., the foreleg, jaw, and maw, which must be given to the priest from every non-sacred animal that one slaughters? Why does he mention teruma alone? The Gemara answers that he could have said to you: In the case of teruma, which has inherent sanctity, and which therefore cannot be redeemed, the priest will not come to err with it and treat it as though it has no sanctity, even if the owner receives payment for it.
הני כיון דקדושת דמים נינהו אתי למיטעי בהון דבר מיתחל קדושתייהו אארבעה זוזי ואתא למינהג בהן מנהג דחולין By contrast, with regard to these gifts of the priesthood, since they have sanctity that inheres in their value, which means that once the priest has received them he may sell them, the priest might come to err with them by saying that the sanctity that they have can be redeemed with four zuz, i.e., the one sela, and he might come to treat them in the manner that one treats non-sacred food. This would be a mistake, as a priest must eat his priestly gifts in a dignified manner, i.e., roasted and with seasoning (see Ḥullin 132b).
אמר רבא תרומת חוצה לארץ אין בה משום כהן המסייע בבית הגרנות רב חמא יהיב ליה לשמעיה § On a related topic, Rava says: Teruma from outside of Eretz Yisrael does not have any prohibition due to a priest assisting at the threshing floor. The Sages decreed that one must separate teruma from produce grown in certain places outside of Eretz Yisrael. Yet, the halakhot governing this teruma are not as stringent as those that apply to teruma from produce grown within Eretz Yisrael. Consequently, one may give such teruma to a priest for helping at the threshing floor. In support of this claim, the Gemara relates that Rav Ḥama gave teruma from outside of Eretz Yisrael to his servant, who was a priest, as his wages.
אמר שמואל תרומת חוצה לארץ בטילה ברוב רבה מבטלה ברוב ואוכל לה בימי טומאתו With regard to teruma from outside of Eretz Yisrael, Shmuel says: Teruma from outside of Eretz Yisrael that became mixed with non-sacred produce is nullified in a majority, unlike ordinary teruma, which requires one hundred parts of non-sacred produce to nullify it. The Gemara relates that Rabba, who was a priest, would nullify his teruma from outside of Eretz Yisrael in a majority ab initio and eat it during his days of impurity. Both of these acts are prohibited in the case of teruma from produce grown in Eretz Yisrael.
רב הונא בריה דרב יהושע כי מתרמי ליה חמרא דתרומה הוה רמי תרי נטלי דחולין וחדא נטלא דתרומה ושקיל חד מיכן ואילך רמי חדא ושקיל חדא The Gemara relates: Rav Huna, son of Rav Yehoshua, when he would happen to have wine of teruma from produce grown outside of Eretz Yisrael, would pour two jugs of non-sacred wine and one jug of teruma wine into a vat in order to nullify the teruma wine, and then take out one jug’s worth of wine to drink. Having done so, from here onward every time he received more teruma wine grown outside of Eretz Yisrael, he would pour one jug of teruma wine into the same vat, which still contained two jugs’ worth of wine, and take out one jug’s worth of wine.
ואמר שמואל תרומת חוצה לארץ אוכל והולך ואח"כ מפריש And Shmuel further says: Teruma from produce grown outside of Eretz Yisrael does not need to be separated before one eats the produce. Rather, one may proceed to eat and afterward separate the teruma from the remainder.
ואמר שמואל אין תרומת חוצה לארץ אסורה אלא במי שהטומאה יוצאה עליו מגופו והני מילי באכילה אבל בנגיעה לית לן בה And Shmuel also says: Teruma from outside of Eretz Yisrael is prohibited only to a member of a priestly household whose impurity comes from his body, e.g., a man who experiences a seminal emission or a menstruating woman. It is not prohibited to a priest who came into contact with a corpse, an animal carcass, or the carcass of a creeping animal. And this statement, that such teruma is forbidden to one whose impurity comes from his body, applies only with regard to eating it. But with regard to touching teruma from outside of Eretz Yisrael, we have no problem with it.
אמר רבינא הילכך נדה קוצה חלה ואוכל לה כהן קטן ואי ליכא כהן קטן שקלה לה בריש מסא ושדיא בתנורא והדר מפרשא חלה אחריתי כי היכי דלא תשתכח תורת חלה ואוכל לה כהן גדול Ravina says: Therefore, a menstruating woman, whose impurity comes from her body, may separate ḥalla from dough outside of Eretz Yisrael, and a minor priest, who has never experienced a seminal emission and is therefore ritually pure, may eat it. And if there is no minor priest available, she takes the ḥalla with the top of a skewer [massa] and throws it in the oven, and then separates another piece from the dough as ḥalla, not because it is necessary but so that the halakhic category of ḥalla should not be forgotten. And an adult priest may eat it, even if he is ritually impure.
רב נחמן ורב עמרם ורמי בר חמא הוו קאזלי בארבא סליק רב עמרם לאפנויי אתאי ההיא איתתא עלת קמייהו אמרה להו טמא מת מהו שיטבול ואוכל תרומת חוצה לארץ אמר ליה רב נחמן לרמי בר חמא The Gemara relates that Rav Naḥman, Rav Amram, and Rami bar Ḥama were traveling in a ferry. Rav Amram went to relieve himself. A certain woman came before Rav Naḥman and Rami bar Ḥama and said to them: In the case of one who is impure through contact with a corpse, what is the halakha with regard to whether he may immerse himself in a ritual bath and partake of teruma from outside of Eretz Yisrael? Rav Naḥman said to Rami bar Ḥama: