It's Not unlawful to make duaa when u r in ur periods. U can even read Quran during the cycle by not touching the Quran with bare hands. Take some neat paak cloth n u can hold Quran with that and read.
somehow i find this really bothering!!!! can periods make a woman SO impure that she cannot touch a book? a book that is lying around on the floors in the ka'aba ground .. where people are also walking on the same floor?
or is it just an exaggerated form of hightened respect and just wrapping it in beautiful cloth and placing it on the highest pedestal ever, and kissing it many times, and sometimes bringing it down to read it ...
how many of us actually just read it as a book which has a world of knowledge in it ... knowledge that you are allowed to receive without any rules and regulations of how to open the book!?
i smell extremism ... sorry ...
but i will add that of course i have grown up with the same rules around me and consciously or unconsciously i also end up following them .. but my brain is still functioning and asks me these questions.