When entering the Khala', the Messenger of Allah would take off his ring.
Sunan an-Nasa'i Book 48, Hadith 174
← Previous Hadith "The Messenger of Allah said to me: 'Say: O Allah, guide me and make me steadfast,' and he forbade me to put a ring on this one and this one" - and Bishr (one of the narrators) pointed to his forefinger and middle finger. And 'Asim said: "One of the two of them."

Sunan an-Nasa'i Book 48, Hadith 173 Next Hadith → "The Messenger of Allah threw away his ring and said: 'I will never wear it again,' and the people threw away their rings."

Sunan an-Nasa'i Book 48, Hadith 175