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Much of our daf is devoted to a description of the plan of The Temple Mount itself, with detailed descriptions of the area from the Ezrat Yisrael (Court of the Israelites) and south of it. The furthest north that a Jewish person who was not a kohen could enter was the Ezrat Yisrael . Kohanim were allowed in the Ezrat Kohanim (The Priests’ Courtyard), as well.
The Altar was defiled by the Seleucid Greeks when they controlled Eretz Yisroel. Later, the remnants of this Altar were taken and placed into the chamber in the northeast corner of the courtyard.
Those familiar with the story of Hanukkah will remember that after recapturing the Temple from the Greeks, Judah Maccabee and his band purified and rededicated the sanctuary. They also saw that the altar itself had been used to offer impure sacrifices to foreign gods. Could it be purified as well?
As the stones retained a degree of holiness and could not simply be discarded. Hence: storage in the Temple in a convenient place which, according to the mishnah in Middot, turned out to be a room off of the Hall of the Hearth.