There are a number of known issues with Google Sync and Apple iOS that are detailed on Google's Mobile Help pages.
One particular issue to note involves deletion behavior: When using Google Sync, if you "delete" a message on your Apple mobile device, the default action is that it will archive the message and not delete it to Trash, as you might expect. To delete the message, you need to select Enable "Delete Email As Trash" for this device in your Google Sync settings. See the complete list of how actions taken on your device affect your Gmail interface when Sync is enabled.
Known Issues >