It varies from Church to Church. Definitely in our Church, women are allowed to clean behind the Iconostasis,and replace the altar linens. I took part in such exercise on the eve of Easter, where we lifted the tabernacle off the Holy Table and the women replaced the linen. Then we placed the tabernacle back. Everyone was lay. The only absolute no-no was when there was any type of Service going on (Divine Liturgy or any other prayer service).
Actually the most important area in a Byzantine sanctuary is the area between the Holy Doors and the Holy Table. Only ordained men may go through that area. Even altar servers or even those ordained to Minor Orders cannot stand in that area. Funny though that the Bishop told me after one Liturgy that I should stand closer to him to hand him the censer. I’m a bit too careful not to enter that area but what happens is that he has to reach out a bit to get the censer.
edit to add:
The nice thing about the Byzantine tradition is that many of the other ministries in church by the laity are done outside the Iconostasis. Women may become a Cantoress or Lectoress because there is never a church architecture where the Cantor would be behind the Iconostasis, nor an area beside the Sanctuary where its looks kind of a gray area if its part of the Sanctuary or not. Also for Lectors, all lay reading are done in the center of the Nave. I’ve heard some would even have the reader stand at the back of the Nave in the middle facing the Holy Doors. But for us the reader just go to the center, or sometimes remain where they are.
