When the duplicate order notification shows up, is it correct to remove those so they do not duplicate the item since it is just relisting after the auction is done?

Yes, the only times you would want to ignore the duplicate checker are:

1. If you had purchased and listed another item with the exact same title as one you currently have in inventory.
2. If you don't use unique sku's and list items with an identical sku to another item that's been recorded in My Reseller Genie

For more information on the duplicate inventory checker, see this article: How sales platform integrations work.