iTunes not showing my previous backups??

Okay so something happened and my iPhone deleted all my contacts. I believe it was somehow connected to iCloud which didnt have any contacts backed up to it so it also wiped my contacts on my phone and pushed the same change to my mac. I tried to restore to a previous back up via iTunes but suddenly the backups before the time at which this occurred don't exist....at least so says iTunes.

I downloaded a trial of this recovery software, "Tenorshare iTunes Data Recovery" which when it scanned my computer for backups found a previous backup and listed all my contacts and info which is what I need! But since its a trial I cant recover more than 3 of these contacts, this program simply recovers them and then saves them as some sort of file. I dont want to pay like $60 though to recover this once though...I also know that the back-ups it list are real and the ones i need because i checked all the contacts and messages it discovered in the scan and they are all there!

Any idea what I can do? Is there a way to search for this back up using a different method and get iTunes to also recognize it so that I can restore my contacts to my iPhone?? The screenshots below show what iTunes is showing and what this program shows

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