The Halachah rules that one must tear his garment when seeing the place of the Temple in ruins (Moed Katan 26a and Shulchan Aruch Orach Chaim #561). In the Beit Yosef when discussing the obligation to rip one’s garment upon seeing the cities of Yehudah and Jerusalem in ruins, Rav Yosef Karo explained that we hold that "in ruins" means "under non-Jewish control." The Magen Avraham (#1) and Mishnah Berurah (#2) accepted this view. This means that even if there is a Jewish settlement in the Land of Israel but it is under non-Jewish control, it is still considered "in ruins", and one must tear his garment upon seeing it. Our Rabbi, Rav Tzvi Yehudah Ha-Cohain Kook, explained that the same applies for seeing the place of the Temple in ruins, and just as "in ruins" means "under non-Jewish control" for the cities of Yehudah and Jerusalem, so too does "in ruins" mean "under non-Jewish control" for the Temple Mount. Therefore after the famous call of "Har Ha-Bayit Be-Yadenu - the Temple Mount is in our hands" during the Six-Day War, he ruled that there is no longer an obligation to tear one’s garment when seeing the Temple Mount, even though the Temple is still destroyed. Our Rabbi explained that it is possible to claim that since there is no Temple, one must tear his garment. One must understand, however, what prevents us from fulfilling the Divine Commandment of "Make for me a Temple" (Shemot 25:8). Our inability to build the Temple is not due to "exile." The Temple Mount is in our hands and we are in control. But we are prevented from building the Temple because of halachic and political reasons. These are our reasons, not those of the non-Jews (Sichot Ha-Rav Tzvi Yehudah – Yom Ha-Atzmaut and Yom Yerushalayim, talk for Yom Yerushalayim p. 90 and Tal Chermon - Moadim, p. 218). Our Rabbi wrote, additionally, that we should also be concerned about ripping our garments when we are not obligated and thus violating "Bal Tashchit" (wanton destruction of items) when the whole prohibition for tearing when seeing the Temple in a destroyed state is a Rabbinic prohibition.
In the book, "Mekor Chaim" (2:95 #1), Ha-Rav Chaim David Halevy - Chief Rabbi of Tel Aviv-Yafo for 25 years - wrote that he agrees with our Rabbi's opinion. He explained that when a close relative dies, we tear our garments when the "dead is before us." After the mourning, we observe an annual Yahrtzeit. Similarly, when our "dead was before us" – the Temple Mount was under non-Jewish control – we had the obligation to tear our garments. Now that we have control, the dead is no longer before us, and we observe an annual Yahrtzeit: Tisha Be-Av. Despite his agreement, Rav Halevy concluded that in order to exempt us from this obligation, the Chief Rabbinate of Israel must make this decision.
It is related what our Rabbi, Ha-Rav Tzvi Yehudah, did on the day when the Temple Mount was liberated: "On the day of the liberation of Jerusalem, our Rabbi and "The Nazir," Rav David Cohain, were together at the Kotel, and the next day our Rabbi went to him to bring him his book "Le-Netivot Yisrael" volume 1 which was published on that very 28th of Iyar 5727. Our Rabbi said that while standing facing the Kotel, he did not tear his garment upon his seeing the place of the Temple since "it is only considered in a destroyed state when the non-Jews rule over it" (Shulchan Aruch, Orach Chaim 561 and Mishnah Berurah #2), and this fundamental principle which was stated regarding the cities of Yehudah also applies to the spot of the Temple. "The Nazir" responded in agreement and added: "Is it not also true that his honor saw that our Master the Rav was there in his Shabbat clothing and he did not tear?" (He had seen a vision of Maran Rav Kook). All were astounded and all eyes turned to our Rabbi, who nodded his head approvingly: "Yes, certainly" ("Rabbenu" - On the Life of Ha-Rav Tzvi Yehudah p. 211).
[Note: In the book "Peninei Halachah" (end of vol. 1 in the second edition), Ha-Rav Eliezer Melamed - Rav of Har Berachah - writes that our Rabbi, Ha-Rav Tzvi Yehudah, would agree today that one should tear his garment upon seeing the spot of the Temple, after the horrible desecration of Hashem's Name which have occurred there. When asked about this, Rav Aviner responded: "Baruch Hashem, the Temple Mount is still in our hands, and with Hashem's help it will remain so," i.e. our Rabbi's ruling still stands that we are exempt from tearing our garments upon seeing the spot of the Temple – M.T.]