This post will show you how to delete mail in your gmail account from the mail.app in your iphone or ipad without archiving it.
1) make sure your iphone or ipad is setup to get your google mail using exchange
2) goto m.google.com/sync in safari on your iphone or ipad
3) click on your device in the list on that page
4) tick ‘enable delete email as trash for this device’
5) click save