Asalamu alaykum wa rahamatu allahi wa barakatu. Is it permissible to correct the Imam of Khubtbah Jumaa during the khutbah. It recently happened and a sister correcting Omar ibn Khatab was the example used to justify the behavior wa allahu alam.
Jazak allahu khiran

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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

In principle, it is obligatory on the attendees of the Friday Khutbah to attentively listen to the Imaam and it is forbidden for them to talk. However, the Sunnah indicated that it is permissible for the listener to speak to the Imaam for a need. It was narrated that while the Prophet, sallallaahu ‘alayhi wa sallam, was giving the Friday Khutbah, a Bedouin stood up and said: "O Messenger of Allaah! Our properties are destroyed and our children are starving. Please, supplicate Allaah for us." The Prophet, sallallaahu ‘alayhi wa sallam, raised his hands for supplication. [Al-Bukhari]

Thus, if the Khateeb (the person who delivers the Khutbah) made a mistake in a Quranic verse or a Hadeeth of the Prophet, sallallaahu ‘alayhi wa sallam, it would be permissible for the audience to correct him, particularly if the mistake is a big one. Shaykh Ibn ‘Uthaymeen said: “If the Khateeb made a mistake which changes the meaning, especially in the Quran, it would be obligatory to correct him. That is because it is not permissible for anyone to change the Words of Allaah The Almighty in a manner that changes the meaning. Such a change cannot be tolerated and the Imaam must be corrected. If the mistake was in his own words, he should be corrected too. For instance, if the Khateeb wants to say that something is prohibited, but instead he says it is obligatory, the listener must correct him. That is because if he is left without correction, people will be misguided, and it is not permissible to agree with the Khateeb on a word which misguides people. However, if the mistake, however, does not change the meaning, it is not obligatory to correct him, such as the grammatical mistakes which do not change the meaning, whether in the Quran or elsewhere.” End of quote.

As for the story in which the woman corrected ‘Umar it was narrated by Al-Bayhaqi and Abu Ya‘la, but the woman contested ‘Umar after he descended the pulpit, not during the Khutbah.