How can Sheikh Ibn 'Uthaymeen's statement that purity is not invalidated by removing the socks be reconciled with the Hadith: "I inserted them while they were pure"? And what prevents wiping over them again after removal? And what is the evidence for the impermissibility of wiping after putting the socks back on?

The difference between the permissibility of wiping over the khuff (leather socks) if worn after ablution and the impermissibility of wiping over them after removing them is that wiping is permissible if the khuff is worn while one is in a state of water purity, i.e., after washing the feet with water, as the Prophet, peace and blessings be upon him, did. It is not permissible to wipe over the khuff after ablution is broken and they are removed, because no scholar has held this view. Otherwise, the prescribed time limit for wiping would have no meaning.