Gmail Exchange Account on iOS: Enable “Delete Email As Trash”
With Google Sync for iOS, the default setting when you Delete email in your iOS Mail app is that Gmail will archive the message and not delete it. When you Enable “Delete Email As Trash” for this device, pressing Delete in your iOS Mail app will delete that email from your device and send it to your Gmail Trash. To enable this setting, go to m.google.com/sync in your mobile browser.
(Source: support.google.com)
