All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
This Hadeeth is reported by a group of scholars among whom is Imaam Ahmad, Abu Daawood and At-Tirmithi . However, some scholars classified it as Dha’eef [unauthentic] while others classified it as Saheeh [authentic] because it was narrated with many routes (chains of narrators). The Hadeeth is evidence that it is not permissible for women to look at men.
Nonetheless, there are other Ahaadeeth that contradict this Hadeeth, saying that this matter is permissible, among which is the Hadeeth by Faatimah bint Qays as the Prophet ordered her to observe her waiting period in the house of Ibn Umm Maktoom as he was blind. Also, the Hadeeth by ‘Aa’ishah when she was looking to the Ethiopians while they were playing in the mosque. Ibn Hajar quoted Ibn ‘Abdul Barr as saying: “The Hadeeth of Faatimah bint Qays is evidence that it is permissible for a woman to look at a blind man and it is more authentic than this one (i.e. the aforementioned Hadeeth).”
Moreover, Ibn Hajar also quoted the statement of Abu Daawood which reads: “This is peculiar for the wives of the Prophet with the evidence of the Hadeeth of Faatimah (bint Qays).” Then Ibn Hajar said: “This is a good reconciliation between the Ahaadeeth, and Al-Munthiri came to the same conclusion in his comments and our Shaykh (i.e. Ibn Al-Mulaqqin ) is of the same opinion and this is a good reconciliation (between the two Ahaadeeth).”
Therefore, it becomes clear that it is permissible for a woman to look at a non-Mahram man; this is of course if this looking is without lust, otherwise it is not permissible for her to look at him with lust according to the agreement of the scholars . However, a woman should lower her gaze from looking at men even without lust as a way of protecting her religion.
To conclude, it is permissible for you to put this screen in the ladies room.
Allaah Knows best.