The British removed their influence and recognized the US as a sovereign nation however they did not remove all of their troops from US lands.
Though the Treaty of Paris 1783 ended the Revolutionary War and Great Britain officially recognized the sovereignty and the independence of the United States. However, they did not remove troops from the US in particular along the western frontier and along the border with Canada. The continued presence of British troops was insulting enough but then the British began attacking US shipping and taking people off the boats to serve in the British army against the French in a system called impressment. These violations of US independence led to the war of 1812 which is considered the "2nd war of independence".