It is narrated from Imam Ibrahim Nakha'i (may Allah have mercy on him) that there is no harm if a menstruating woman picks up something from the mosque.
Hadith Referenceسنن دارمي / من كتاب الطهارة / 1199
It is narrated from Ata’ (may Allah have mercy on him) regarding a menstruating woman taking something from the mosque, he said: She may pick it up except for the Mushaf (copy of the Qur’an).
Hadith Referenceسنن دارمي / من كتاب الطهارة / 1202