Q: Restoring new iPhone.

Unless you can remember the password for that backup, you can not use it. I suggest that you just keep trying passwords that you think you might have used until such time that you get totally frustrated and decide to move on. You don't get locked out after too many attempts, you just can't use the backup,

if you find your self in the situation where you can not get the password, delete the backup and just move on. If you keep the encrypted backup, the phone will continue to backup and overwrite the encrypted backup and it will be unusable.

It appears that at some point the backups were encrypted and if so this is all you can do:

If you forgot the Encryption Password:

https://support.apple.com/en-us/HT205220

Charlie6ton wrote:

 

I am attempting to restore my new iPhone from an old backup on my computer. I never used a password for backups of my old phone but I am now being asked for one. Any suggestions how to proceed? Thanks.

If it is asking for the encryption for your iTunes backup, and you don't know it, then you won't be able to use it.

there is no way to bypass that.

As this article says:

"If you forgot your password, the only way to turn off backup encryption on your device is to erase the device and set up as new."

About encrypted backups in iTunes - Apple Support

The only fortunate thing is that you get an unlimited number of guesses of passwords for encrypted backups.  I have read in past threads that some people who swear they never set a password have had success by trying a "blank" password - either one or more spaces or simply hitting the "enter" key.  There is no harm in trying.

Demo wrote:

Unless you can remember the password for that backup, you can not use it. I suggest that you just keep trying passwords that you think you might have used until such time that you get totally frustrated and decide to move on. You don't get locked out after too many attempts, you just can't use the backup,

 

if you find your self in the situation where you can not get the password, delete the backup and just move on. If you keep the encrypted backup, the phone will continue to backup and overwrite the encrypted backup and it will be unusable.

Please correct me if I am wrong. 

Your first paragraph is right on of course. The OP may well be able to guess the PW again by trying things he might have used. However I was under the impression (perhaps wrongly) that even if he were to delete the backup from the computer, the next time he tries to backup again the new backup will be encrypted as well. The code to encrypt, to my knowledge, is stored in the phone itself, not the backup. I believe that all the OP can do in the event that he cannot remember the PW is erase the phone. Is this wrong?

And actually it is wrong. I just remember another option for the OP but not for the faint of heart:

To bypass the issue of encrypted backups always being encrypted:

Backup to iCloud. Then erase the phone. Then backup to iTunes as an unencrypted backup. Then restore from the iCloud backup. Then backup to iTunes again.

From: https://discussions.apple.com/message/30209896?tstart=0#30209896

I stand corrected. Thanks!

One way or the other, the phone has to be erased according to what Gail was saying. I remember that discussion, however, I think that she talked about the password being tied to the device itself in another thread, maybe in the lounge?

The phone will have to be erased and set up as new. But using Gail's method allows you to create a backup and use it after erasing the device. If you erase the device completely, there is no way that the encryption code can still be tied to the device

Demo wrote:

 

The phone will have to be erased and set up as new. But using Gail's method allows you to create a backup and use it after erasing the device. If you erase the device completely, there is no way that the encryption code can still be tied to the device.

I agree, of course....

On another read of what I previously wrote I now realize that what I said before was not clear, I did not use good words. By "And actually it is wrong." I meant I was wrong, not you. I was referring to the paragraph I had written right before where I said that there were no other options. The Gail method is another option.

You are welcome, good luck.