Praise be to Allaah.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen answered this question as follows:
The partition should stay. The fact that there was no partition at the time of the Prophet (peace and blessings of Allaah be upon him) was either because there was no need for it or because there was a reason why they could not have a partition. With regard to the former, the Sahaabah, may Allaah be pleased with them, had such strong faith in Allaah that they would not look at women; with regard to the latter, the financial situation of the Sahaabah, as we know, especially before the conquests, was one of hardship, and they could not afford to put a partition between themselves and the women. Having understood this, we should next look at which is further removed from fitnah, having a partition or not having it? Everyone will agree that having the partition is less likely to cause fitnah. If that is the case, then whatever is less likely to cause fitnah is what should be done. If you say, “If we insist on keeping it, those who want to remove it will stay away from the mosque,” our response is that if they stay away, they are doing wrong. They have no excuse for failing to pray in jamaa’ah because of this partition being there. Having the partition there is not a sin such that they could say, “We are not coming to be witnesses to sin.” If they stay away, they are committing sin by failing to attend prayers in congregation.