Performing Salaah With Dirty Shoes

Discovering impurity on clothes after finishing Salaah does not invalidate the Salaah, and there is no need to repeat the previous Salaah, if you were ignorant or unaware of it or if you forgot that your clothes have an impurity. This is based on the Hadeeth of the Messenger (Sallallahu Alaihi Wasallam - Peace and blessings be upon him) when he was leading his companions (Radiallahu Anhum - May Allah be pleased with them) in Salaah, when he suddenly removed his shoes and put them to his left side. When people saw this, they removed their shoes. When the Messenger (Sallallahu Alaihi Wasallam - Peace and blessings be upon him) finished his Salaah, he asked them: “What made you remove your shoes?” they said: ‘We saw you remove your shoes, so we removed our shoes’. The Messenger (Sallallahu Alaihi Wasallam - Peace and blessings be upon him) said: “Jibreel came to me and told me that they carry an impurity, [or he said “harm”]”. [Reported by Ahmed, Abu Dawood, and others].
As it is clear, the Messenger (Sallallahu Alaihi Wasallam - Peace and blessings be upon him) did not stop his Salaah, nor repeat it. But just removed his shoes and continued his Salaah. Please explain.