Exporting produce with kedushat shevi'it
The Mishnah (Shevi'it 6:5) states that it is forbidden to take produce with kedushat shevi'it outside of the Land of Israel.
There are several rationales behind this prohibition:
The Torah states (Vayikra 25:6): "And the [produce of] the sabbatical year is for you to eat". Chazal learn from here (Pesikta Zutrata, Vayikra, Behar 70b) that it is for us, the Jewish People, and not for others. For this reason, shemitah produce should not be exported since mainly non-Jews would eat them.
Another rationale is that bi'ur must be performed in the Land of Israel. This we learn from the phrase in the next verse (25:7) "And for your domesticated and wild animals in your land ..."
Exporting produce without kedushat shevi'it and etrogim
It is permissible to export produce without kedushat shevi'it. This includes:
Flowers not grown for their fragrance
Produce grown on land sold to non-Jews through heter mechirah
Shemitah produce grown in hothouses on detached platforms
If necessary, there are posekim who are lenient with exporting produce with kedushat shevi'it either after bi'ur time or long before bi'ur time, so that the produce will no longer be there during bi'ur.
Etrogim
It is also possible to be lenient when the produce is exported primarily for Jews (such as etrogim for the arba minim - this will be relevant this coming Sukkot, 5783).
However, when purchasing a shemitah etrog, it is important to make sure that it is no longer around at bi'ur time. For this reason, it is recommended to prepare jam from your etrog and eat it before bi'ur time.
Taking kedushat shevi'it produce with you on a plane
You are not supposed to take kedushat shevi'it produce outside the Land of Israel.
What about an individual traveler taking food for the way on a flight abroad?
In light of the two rationales we saw earlier this week, we can understand the answer:
We do not want kedushat shevi'it produce to reach non-Jews, AND Bi'ur must be performed in Israel.
Thus: Travelers may take kedushat shevi'it produce with them for personal consumption.
Of course, avoid taking dried dates or other foods right before their bi'ur time.
