I believe the List that is used for selection and the list that in the bottom with duplicates are 2 separate lists
Are you check if Parent 1 is already added. and only add if it is not added. By default List Allows Duplicates, so it is your responsibility to check and verify if the element is already present or not before adding
you can do a Find by Expression on the bottom List and check if Parent 1 already exists. if not then add it and refresh in client. so it wont be duplicated