Tosefta zu Wajikra 23:22

Said Rabbi Shimon, because of four things the Torah said not to give a person Peah except at the end of his field: [First,] due to theft by the poor; and [second,] due to waste by the poor; and [third,] for appearance's sake; [and fourth,] due to the deceivers. Due to theft by the poor -- how so? That they will not see a time that there isn't someone there [guarding the field], and he [?] will say to the poor person, "Come and take Peah." Due to waste by the poor -- how so? That there will not be poor people and sit around and watch the whole day and say, "Now give [us] Peah!" whereas when Peah is given at the end, he goes [about his business] and does his work, [and then] he comes and takes it at the end. For appearance's sake -- how so? They will be there and pass through and say that they saw so-and-so that harvested the field, and did not give from it Peah, that behold the Torah said (Lev. 19:9), "you are not to finish [to the] edge of your field in harvesting." Due to deceivers -- how so? That they will not say, "We already gave [Peah]." Or another version, that [the homeowner] will not leave the good and give the bad.

[There are] four gifts [for the poor] from the vineyards: Peret (i.e., grapes that fall during harvesting, see Lev. 19:10, Peah 7:3), forgotten sheaves (Deut. 24:19), peah (Lev. 23:22), and olelet (i.e., defective clusters, see Lev. 19:10, Peah 7:4). [There are] three [gifts for the poor] from field-produce: Gleanings (Lev. 19:9), forgotten sheaves, and peah. [There are] two [gifts for the poor] from fruit trees: forgotten sheaves and peah. [And as to] all of these, they should not [be given as] a favor, and [others] can even take [gifts for the poor given as a favor] from a Jewish poor person from his hand (i.e., since it does not lawfully belong to him in the first place). And [as to] the remainder of the priestly gifts, such as the shankbone and the jawbone and the rough-stomach (see Deut. 18:3), these may be [given as] a favor. And we give [these] to every Kohen that desires [them].