Transferring data to new iPhone

Sounds as if you have an encrypted backup. If that is the case and you do not remember the password, then you will not be able to use that backup. Placing a password on a backup requires the entry and a verification, so it cannot be done accidentally. You will have to delete the backup in iTunes. If you still have the old iPhone, try creating another backup, but make sure that the Encryption box is not checked before you make that backup. If you cannot make another backup of the old device, you will have to set the phone up as new, without the backup. About encrypted backups in iTunes - Apple Support

In iTunes, you delete the backup by going to Edit>Preferences>Devices, then select the backup and delete it. You cannot un-check the encryption box until you have deleted the encrypted backups and wiped the phone.

What exactly is locked, and what is the exact text of the error that you are seeing? Where is it asking for a password/passcode?

Do you mean the data transferred is locked by a password?