Is it permissible to interrupt a supplication for someone who greeted or called out?

Scholars differed on the ruling of greeting one who is reciting the Qur'an, performing dhikr, or supplicating (making du'a). Some held it to be recommended and that responding to the greeting is obligatory. The Shafi'is, however, excluded one who is deeply engrossed in recitation or supplication with his heart, stating that it is disliked to greet such a person and that responding to the greeting is not obligatory for him.

The Hanbalis held it to be disliked to greet them for fear of distracting them, and one who greets them in this situation is not entitled to a response.

As for responding to a mother's call, it takes precedence over continuing with supplication; in fact, it becomes obligatory if the mother is inconvenienced. For honoring parents is obligatory and takes precedence over what is recommended, and it takes precedence over a collective obligation (fard al-kifaya). The supplication can be resumed after fulfilling the mother's need.