Question: I inadvertently bought some yellow peppers that are from Israel. What should I do with them?
Answer: There is a machlokes in the Gemara (Moed Katan 2b) as to whether the observance of shemitta nowadays is mideoraisa or miderabanan. According to the Ramban (Sefer Hazechus, Gittin 36) and the Raavad (Shemitta Veyovel 1:11) shemitta nowadays is mideoraisa, while according to the Baal Hamaor (Sefer Haterumos 45) it is only a midas chassidus (pious act). Most rishonim (Rashi; Tosafos, Gittin 36a) though, understand shemitta nowadays to be miderabanan (See Gra YD 331:6).
Regardless, during the shemitta year, we are forbidden to do business with shemitta produce (Avoda Zara 62a), to destroy it (Pesachim 52b) and to remove it from Israel (See Igros Moshe OC 1:186).
As opposed to fruit, even though most of the vegetable growth may have been before shemitta, the determining stage for vegetables is the time it was picked. Thus, as the peppers you bought were picked in shemitta, all the rules of shemitta produce apply. For a full list, see http://www.kosher.org.uk/article/shemitta-dates
As one isn’t allowed to destroy shemitta produce, one can’t simply throw one’s leftover shemitta food away. Rather, one must place it in a designated place until it rots and becomes inedible before disposing of it.
Some poskim (Rabbeinu Tam, Tosafos, Sukka 39b) forbid one to eat produce that has been guarded and worked on (shamur vene’evad), while others allow one to benefit from such produce (See Igros Moshe OC 1:186).Modern day poskim thus advise that either one eats such produce and disposes carefully of any leftovers, letting them rot first, or disposing of them all in such a way without partaking of them.