You can hide any outgoing or incoming item from the default view by archiving it. Recipients can still respond to archived items.
As the confirmation window says, the item is removed from the list of outgoing or incoming items. If you need to see an archived item, select Show all + archived items in the upper right corner of the Outgoing or Incoming tab.
If you want to un-archive an archived item, click the check box next to the archived item and click the Un-archive button.