Praise be to Allah.
We do not know of any du’aa’ in the saheeh Sunnah that is like the one mentioned by our sister.
It is not permissible for anyone to attribute to the Messenger (peace and blessings of Allaah be upon him) things that he did not say. The Prophet (peace and blessings of Allaah be upon him) said: “Whoever tells lies about me deliberately, let him take his place in Hell.” Narrated by al-Bukhaari, 1291; Muslim, 933.
Not every hadeeth that a person hears or reads in a book is saheeh, rather he must verify whether the hadeeth was indeed narrated from the Prophet (peace and blessings of Allaah be upon him), and it should be taken from trustworthy scholars who have sound knowledge of the hadeeth of the Messenger (peace and blessings of Allaah be upon him).
It was narrated by Muslim in the introduction to his Saheeh (5), and by Abu Dawood (4992) that the Messenger (peace and blessings of Allaah be upon him) said: “It is sufficient lying for a man to speak of everything that he hears.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Because usually he hears both true and false things, and if he were to speak of everything that he hears, he would be lying because he would be telling of something that did not happen. End quote.
It is permissible for a menstruating woman to remember Allaah by reciting whatever du’aa’s and dhikrs she wants; there is no reason why she should not do that. And it is permissible for her to recite Qur’aan, as is the view of Abu Haneefah and the view favoured by Shaykh al-Islam (may Allaah have mercy on them both).
Shaykh al-Islam Ibn Taymiyah said in Majmoo’ al-Fataawa, 26/190:
There is no basis for saying that she (a menstruating woman) is not allowed to recite Qur’aan. The quotation, “The menstruating woman and the one who is junub should not recite Qur’aan” is a weak hadeeth, according to the consensus of the scholars who have knowledge of hadeeth.
Women used to menstruate at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him), and if reciting was haraam, as prayer is, this would have been something to which the Prophet (peace and blessings of Allaah be upon him) drew the attention of his ummah, and the Mother of the Believers would have known it, and that would have been something that was transmitted to the people. Since no one narrated any such prohibition from the Prophet (peace and blessings of Allaah be upon him), it is not permissible to make it haraam when it is known that he did not forbid it. Since he did not forbid it even though there were plenty of menstruating women around at his time, then it is known that it is not haraam. End quote.
But she should recite Qur’aan without touching the Mus-haf, either by reciting what she knows by heart, or reading from the Mus-haf whilst wearing gloves or something similar that will prevent her from touching the Mus-haf directly.
See also question no. 6564
And Allaah knows best.