Q. Can a woman that removed a Mezuza for having it chequed place it back also? Does she make a bracha then?

A. On question 3943 regarding if a woman living alone, can place a mezuza on the entrance of her home,w e wrote:
“Poskim disagree. Yeshuos Malko (H. Mezuza 5: 10) rules that although a woman is obliged in the mitzva of mezuza, she should not affix it in its place herself, as this is similar to writing the mezuza, which she is not qualified to do. Teshuvos Vehanhogos (4:238), Shaarei Hamezuza (16: 6) and others maintain that on the onset, a woman should not affix a mezuza. Beer Moshe asserts that if done, the mezuza should be removed and replaced by a man without a bracha.

However many Poskim permit. Birkei Yosef asserts that since she is bound to keep this mitzva and she is not allowed to dwell in a home without it, if she was not permitted to place the mezuza herself, she would also not be permitted to make an agent or shaliach to do it for her. The reason being that you cannot have a shaliach perform something for you, if you cannot do it yourself. (Gittin 23b).

Chasam Sofer (Y.D. 210, Eretz Zvi (15), Daas Cohen (169), Yabia Omer (3: 18), Chovas Hadar (9: 3) are some of the Poskim that permit women to affix mezuzos.
Horav Shlomo Miller’s Shlit’a opinion is that a woman may place lekatchila (on the onset) a mezuza with a brocho.”
See also question 3943

Horav Dovid Pam Shlit’a mentioned that she should be careful when reciting a brocho, that it is placed back on the day after, as mentioned in Aruch Hashulchan (289: 4)
.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu and Horav Kalman Ochs Shlit’a