Question: Is it possible to remove the closed assignments from the Manage Assignment Queue in the user experience WebApp
Yes. Make a Request Inactive on the Admin Portal side, in the Requests area.
It will hide it from the Requests tab in the Manage Assignment widget when in the WebApp UI. (It will not remove it from submissions)
*Note: Also, when you make an Assignment inactive it will remove it from the Assignments tab in UI under Manage Assignments, so it is not available to be assigned.