Is تحية المسجد (the prayer of greeting the mosque) to be offered again after renewing one's ablution and leaving the mosque, then returning to it, given that the place for ablution is very close to the mosque and may even be inside it?

If a worshiper's ablution (wudu') breaks while they are in the mosque, and they leave to perform ablution in a nearby or connected place, it is recommended for them to repeat the "Tahiyyat al-Masjid" (greeting of the mosque) upon re-entering. This is the view preferred by some scholars, such as Al-Nawawi and Sheikh al-Islam Ibn Taymiyyah, who believe that the greeting of the mosque is recommended every time a Muslim enters the mosque, even if their entry is repeated within the same hour.