I need for my app to login using TouchId, but I don't want the user to select or fallback into Password option. In other words I'd like to hide the 'Enter Password' label in the figure below. Thanks.
As far as I know there is no way to hide the password option. Although you can use the device passcode as the fall back.
Please note that the terminology "Passcode" and "Password" refers to different thing in TouchID integration.
"Password" is used for LocalAuthentication approach for integrating TouchID and refering to the applications password as fallback method.
While "Passcode" is referring to the passcode to unlock the device and authenticate purchase in app store.To use the method, you have to store some information to the device's keychain and retrieve it via Touch ID authentication.
See more about these two approaches here
iOS 9 Edit
Based on this answer, iOS 9 provide a new option to hide the passcode option.
For iOS 9, two new policies have been added that do not fallback to passcode. These policies are kSecAccessControlTouchIDAny and kSecAccessControlTouchIDCurrentSet