Is wudu' obligatory for sitting in the mosque?

Question:
If a person sits in the mosque to attend a lesson or the like, and then his wudu' is broken, is he obligated to renew his wudu'?

Answer:
No, it is not obligatory. However, if he is in a state of major ritual impurity, he may not sit in the mosque. But if he is not in a state of major ritual impurity, even if he is not in a state of ritual purity, he may sit and listen to the lesson and benefit, even if he is not in a state of ritual purity. Except for the one in a state of major ritual impurity; no, the one in a state of major ritual impurity may not sit until he performs the full ritual bath.
Q: What if he returns to pray two rak'ahs?
The Shaykh: If he returns to pray two rak'ahs, that is the sunnah of wudu' and the greeting of the mosque.
Q: ...?
The Shaykh: It indicates that it is not obligatory, meaning that the five prayers are the obligatory ones, and the rest are sunnah. The greeting of the mosque and others are all sunnah.
Q: ...?
The Shaykh: It does not harm from the perspective of handkerchiefs; it does not harm, there is nothing wrong with it.