What is more befitting when entering the mosque to make up a missed prayer: to begin directly with the missed prayer, or to pray two rak'ahs for greeting the mosque first, and then make up the missed prayer?

"Tahiyyat al-Masjid" (greeting of the mosque) is achieved by any prayer, whether obligatory (fard) or supererogatory (nafl). Its purpose is to occupy the space with prayer before sitting down. If the person entering prays with the intention of fulfilling an obligatory prayer and "Tahiyyat al-Masjid," his prayer is valid, and he achieves both the obligatory prayer and the greeting simultaneously. Therefore, it is preferable to begin with a missed prayer (qada') because it deputizes for the greeting.