Removing the Activation Lock will require you to submit the original purchase receipt from Apple or Authorized Apple seller. The boxes make no difference and does not prove anything. If the scammers placed your device in Lost Mode, the lock will not be able to removed. Submit your original receipt here:
https://al-support.apple.com/#/additional-support
Of course you should never enter anyone else's Apple ID into your phone. You are basically turning over your phone to them. You can contact Apple directly, but they are likely to refer you to the link provided above.
Contact Apple for support and service - Apple Support