However, a cut-up thigh should not be sent, because a Jew might buy it. But how could a Jew buy presumably non-kosher meat from an idolater? - We are dealing with a place where the majority butchers were Jewish, and when a non-kosher slaughter (terefah) occurred, they announced it. Jews then would refrain from buying from a re-seller on that day.
Another reason that a cut-up thigh may not be sent is that a Jew would then be deceiving an idolater, who would think that he got a super kosher piece of meat, and deceiving any person (literally, "stealing his mind") is prohibited. One should not accustom himself to sleekness and enticement, and even one deceiving or misleading word is not allowed.
Art: Francisco De Goya y Lucientes - A Butcher's Counter