For Groups API, I'm assuming you're trying to post to groups using the Channel feature? Generally, you shouldn't need to go through the review process *if* the Group admin is also an admin of the Facebook Application. If that's the case, then you can switch your app to 'dev' mode, authenticate on the front-end to grant the permission on login, and then switch back to live mode. The permission should still be granted then.
If you're needing the Group permission so that you can post to regular user's Group pages, then yes, you'll need to go through the full review process. You'll need to show exactly how you'll be using the group permission, like setting up channels and posting to your users groups.. That is more complex, but if that's what you're trying to do, it's a step you'll need to take.
I hope that helps explain, but if you still have issues, please let us know.
Thanks,
Alex