Our Gemara on Amud Aleph teaches that ordinarily sums of money below a perutah are not legally pursuable, such as theft of less than a perutah.  Yet, when it comes to the Temple treasury, one must pay restitution for even less than a perutah.

Yismach Moshe (Mattos 6:2) uses this idea to explain why a gentile who steals from a Jew even less than a perutah is still held liable. The reason why theft of less than a perutah is not legally liable for a Jew is because the standard assumption is he forgives such an insubstantial amount (see Rashi Eiruvin (l62a, “Ben Noach”). If so, why would the Jew not forgive the theft of less than a perutah even if perpetrated by a gentile? Yismach Moshe says that even though it is not prosecutable as theft, it is a transgression and violation of the Jewish person’s sovereignty, akin to violation of the Temple treasury, and thus subject to penalty even for less than a perutah. 

I believe there are two simpler answers to the question. We could say that Rashi holds that a Jew only forgives theft of less than a Perutah to a fellow Jew who treats him the same. This is along the lines of the verse in Mishley (29:17):

As face reflects a face in water, so does one man’s heart to another.

Perhaps the Yismach Moshe felt that an easygoing and generous attitude toward money is a character trait that comes from a certain internal disposition. Therefore if one has a tendency to forgive a certain amount, it is not contingent on anyone else’s behavior. 

Regardless, Yismach Moshe explains further, that since it is still less than a perutah it also should be below what is considered a legal threshold, and not have a status of a violation. This can be compared to one who eats less than an olive’s volume of non-kosher food, for which he is not legally liable. However, he cites the Rambam (Laws of Kings 9:10) who holds a gentile is punishable for violating the Seven Noahide laws with no minimum threshold. Therefore, theft of any amount is liable.

We might wonder why does the Torah not enforce matters below a minimum threshold for Jews and not gentiles? This is not just about monetary forgiveness as the same would ruling of the Rambam applies to eating a limb taken from a live animal. Both Jew and gentile are forbidden to eat from it, but for a Jew the minimum punishable violation would be consumption of an olive’s volume, but for a gentile there is no minimum.

I believe the answer is to this is based on distinctions in the underlying relationship. A Jew has a covenantal obligation to follow the mitzvos, thus he is subject to legal definitions and parameters. In this regard, at least as far as administration of punishment by Jewish courts, all laws by definition are subject to definitions and limits. However, the gentile must follow the Seven Noachide Laws as a matter of basic obligation and God’s decree of fundamental human morality. There is no threshold for fundamentals, and any break is a transgression. The transgression is not based on a legal stipulation but instead is regarded as deviating from basic acceptable morality.