IPhone 4 with IOS 7 backup files cannot restore to 3GS

I updated my IP4 to IOS 7, backup my files, restore my IP4 to factory settings, and then gave it to my mum, assuming that I could restore all my data on my spare IP3GS.

Itunes stated that my 3GS needs to be updated to a newer version. Therefore, I am unable to sync my backup data to my 3GS.

Are there any alternatives to restore the backup files back to the 3GS?