Shavua Tov. Yesterday ספירת העומר was 21.
On the very first Pasuk in פרשת אמור, the תורה תמימה brings a commentary from the ירושלמי that says that a male Kohein is not allowed to go to חוץ לארץ but a בת כהן is allowed.
This is learned from the words בני אהרון where it literally means the sons of Aaron but not the daughters.
The Rambam explains that the Rabbis made a decree regarding what they called, טומאת העמים, the impurity of the nations.
Therefore, anyone who left Israel would be defiled and would need to go through purification of at least a Mikva. The debate was whether this applied even to the אויר, the “air” of חוץ לארץ or only the land.
This would mean that if a Kohein put his תרומה in the air space of חוץ לארץ, it would be defiled and needed to be burned.
Even though the laws of טומאה and טהרה applied mainly during the time of the Temple, Kohanim need to be more careful about leaving Israel- even on Pesach!