Feeding the Cleaner in Israel and Yourself in the USA

Rina from Ramot asks:
I sometimes make a vegetable quiche. In the past, I have often served a slice to my non-Jewish cleaning help. May I continue to do so if the vegetables are sh’mittah produce? If she asks for a slice to take home for her husband, may I give it to her?
The Torah states that sh’mittah produce should be eaten, and not destroyed. Feeding to non-Jews is, for the purpose of this law, considered a form of destruction. A non-Jew can not be trusted to treat the food in accordance with laws attached to its sanctity. The exception to this rule is feeding your non-Jewish worker while he is on the job or otherwise a guest at your table. Since he is eating under your supervision, you will ensure that the relevant halachos are kept. So you may continue serving vegetable quiche to your cleaner, but do not send a slice to her husband!
Matty from Mattersdorf asks:
I often travel by plane. I do not always receive airline meals with a hechsher (kosher certification) that I trust. Furthermore, the doctor has put me on a strict diet and these meals sometimes contain ingredients which are off-limits for me. May I take some sh’mittah vegetables (or fruit, when it becomes available) as provisions for my journey abroad?
It is generally forbidden to export sh’mittah produce. The reason given is that we are concerned that any leftovers will not be disposed of correctly at the appropriate time (bi’ur). However, in cases of need, a small amount may be taken with as provisions for a journey. Since the amount is small, we can safely assume that it will be consumed before the time of bi’ur arrives (Source: Rav Shlomo Zalman Auerbach and Rav Elyashiv). The Chazon Ish also permitted the export of sh’mittah esrogim for the mitzvah. However, he stipulated that they must be returned to Eretz Yisroel for bi’ur.