Get rid of "Exported service does not require permission" warning
The warning is telling you that you have exported (ie: made publicly available) a service without securing it with a permission. This makes your service available to any other applications without restrictions. See Exported service does not require permission: what does it mean?
If your service doesn't need to be available to other applications, you don't need to export it. Explicitly setting android:exported="false" will remove the warning.
Note: The default value for android:exported is true if you have provided an Intent filter.
You need to add a permission requirement for your service. The one you need is android.permission.ACCOUNT_MANAGER. Your authenticator is only accessed through the manager.
Regarding this issue, there is already a bug created in Android project about this warning using "Sync Adapter": https://code.google.com/p/android/issues/detail?id=37280 but it's still an Open bug.