They broke it open, and after the later conquests the place was left to serve as a mosque. The people of distinction among our shaykhs would not pray anywhere within that entire structure and would instruct their followers to refrain from doing so, in obedience to the command of the Messenger of Allah, peace and blessings be upon him, and so as not to incur his displeasure, as mentioned above.
Likewise, lighting lamps at these shrines under any circumstance is impermissible—on this point I know of no disagreement—for it is explicitly forbidden. It is also unlawful to fulfill any vow to provide them with oil or anything else, for such a vow carries the same ruling as a vow to commit sin.
Among the prohibited matters is performing the prayer at the site—even if no mosque has been built there—for that too constitutes turning it into a mosque, just as ʿĀʾishah said:
“Had it not been for that, his grave would have been left open, but they feared it would be taken as a mosque.”
ʿĀʾishah, may Allah be pleased with her, did not merely mean the erection of a building, for the Companions would never have built a mosque around his grave. Rather, she meant that they feared people would pray at his gravesite. Every place that people intentionally choose for prayer thereby becomes a mosque; in fact, any spot where prayer is performed is called a mosque, even if no structure stands upon it, as the Prophet, peace and blessings be upon him, said:
“The entire earth has been made for me a place of prayer and a means of purification.”
Abū Saʿīd al-Khudrī also reported that the Prophet, peace and blessings be upon him, said:
“The whole earth is a mosque, except for graveyards and bathhouses.”
This ḥadīth was related by Aḥmad, Abū Dāwūd, al-Tirmidhī, Ibn Mājah, al-Bazzār, and others through sound chains. Those who criticized it have not examined all of its transmission routes.