What gave up its claim to the Oregon Territory in 1820s when Monroe Doctrine closed American continents further colonization?

There is no mention of the Monroe Doctrine in your question, so I cannot provide the answer. However, the Monroe Doctrine is a United States policy that was issued on December 2, 1823, by President James Monroe. The Monroe Doctrine warns European nations not to interfere with the affairs of the Americas, stating that any new European colonies or interference with existing colonies would be viewed as acts of aggression that could lead to war with the United States.