Do I need to remove the entire interior cover to change the batteries on the Home Connect 620?

No, you do not need to remove the entire interior cover to change the batteries.  Remove the security screw securing the black RF window to the interior cover so the black RF window can be pushed up to expose the battery pack tab.  Use the tab to pull the battery pack up for quick access to the batteries.  For detailed instructions on how to remove the security screw, please see installation guide.