[whpalmer4]

Ah, now the setting for the Inbox does sync from the Mac. In the preferences on the Mac, in the Data section, there's a checkbox for Clean up completed Inbox items. If that is checked and the Mac and iPhone are synced, the iPhone should hide completed items in the Inbox. General practice is that one moves actions off into projects before doing them (unless they are trivial), but as you've seen, it is certainly possible to mark Inbox actions as completed without doing so.