Yes it is as safe as anything can possibly be on the iPhone.
Consider:
- Apple does not do security review of the submitted apps, but they do remove from the appstore the apps known to violate privacy. If the app you are using has been out for some time it's probably OK.
- Memengo, Inc, the developer of GeeTasks, has been also developing and selling Memengo Wallet (a dedicated password management app for iPhone). We've been in business of trust and securty since the beginning of the app store, for over a year now. Thousands of users are enjoying the convenience and security of it.
- Your Gmail password is stored in iPhone's keychain just like any other password is stored on the iPhone (e.g. your GMail or mobileme password).
- You Gmail password is only ever sent to Google for login, and is not sent to anywhere else
- I also wrote some extra code to make sure that your password does not end up in the logs or crash dumps.