Is the "greeting of the mosque" (tahiyyat al-masjid) obligatory for someone who exited to the mosque's courtyard and then returned?

Greeting the mosque (Tahiyyat al-Masjid) is a Sunnah according to the majority of scholars, not an obligation. Performing Tahiyyat al-Masjid once is sufficient, and there is no need to repeat it if the person entering has not left the mosque's outer fenced courtyard. However, there is no harm if one does repeat it.