Must one who has removed his socks for moments after nullifying his ablution wash his feet again upon redoing the ablution?

It is not permissible to wipe over socks during ablution (wudu') unless they were put on while one was in a state of complete ritual purity (tahara). The prophetic tradition (Sunnah) indicates this, as narrated by Al-Mughirah ibn Shu'bah, that the Prophet (peace be upon him) said concerning his khuff (leather socks): "Leave them, for I put them on while my feet were pure." So he wiped over them.

Scholars have reached a consensus on the condition of prior purity for the permissibility of wiping. Therefore, if a person removes his socks and then puts them back on without being in a state of purity, it is not permissible for him to wipe over them; rather, he must wash his feet during ablution.