Thabit ibn 'Ubayd narrated from al-Qasim ibn Muhammad, who said:

'A'ishah said: The Messenger of Allah, peace and blessings be upon him, said to me: "Hand me the khumrah from the mosque." She said: I said, "Indeed, I am menstruating." He said: "Indeed, your menstruation is not in your hand."(1)

Regarding this chapter, there is also a narration from Ibn 'Umar and Abu Hurayrah.

The hadith of 'A'ishah is a hasan hadith.(2)

This is the view of the generality of the people of knowledge; we know of no disagreement among them on this matter: that there is no harm in a menstruating woman taking something from the mosque.

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(1) Sahih. Narrated by Muslim (298), Abu Dawud (261), Ibn Majah (632), and al-Nasa'i 1/146 and 192. It is in al-Musnad (24184) and Sahih Ibn Hibban (1357).
"Al-khumrah": it is the mat upon which the worshipper prostrates. It is said that it was called khumrah because it covers (tukhammir) the face of the worshipper from the ground, i.e., it conceals it.
His saying, "Indeed, your haydah": with a fatha on the ha'. Al-Qadi 'Iyad said in Mashariq al-Anwar 1/217: This is how the narrators and jurists have recorded it, with a fatha on the ha'. Abu Sulayman al-Khattabi claimed that the correct form is with a kasra on the ha', like qi'dah and jalsah, meaning the state of menstruation or its name. Al-Qadi, may Allah have mercy on him, said: What I hold is that what the majority have is correct, because the Prophet, peace and blessings be upon him, only negated from her hand the menstruation that is the blood and impurity which must be avoided and deemed repugnant. As for the ruling of menstruation and the state that characterizes a woman, it is necessarily attached to her hand and her entire body. The fa'ilah form is only used for the postures of actions, like qi'dah and jalsah, not for rulings and states.
(2) Added here in the edition of Shaykh Ahmad Shakir: "Sahih," and it is in the copy of al-Mubarakfuri, and was added in (S) in a different hand, and it is not in the rest of our relied-upon manuscript sources, nor in the two copies of Ibn Sayyid al-Nas and al-Mizzi.