Can't see TIB files from bootable recovery

Joe, welcome to these User Forums.

More questions at this point than answers:  "I have two backups, both encrypted."

How are these backups encrypted? 

If this is by using the Advanced Options > Password protection encryption for the backup task that created these files, then there should be no issue.

If the backups or the storage drive are encrypted by some other method, such as BitLocker, then the Acronis Rescue media does not have any means of opening such encrypted drives / backups.

See KB 56619: Acronis True Image: compatibility with BitLocker which gives more information on the above.

How is the backup drive connected to your computer?

Is this a local USB drive or is it a network drive? 
If a network drive, how are you connecting to that drive when booted from the Rescue Media?
If you are using wireless, then again the Rescue Media has very little support for wireless adapters (but this seems unlikely given you say you were able to select the drive to look for the .tib files).

They're encrypted using the backup protection option using AES 256 encryption in True Image. The external hard drive is connected through usb to my computer.

Joe, if this is just Acronis password encryption, then there should be no issues in seeing / opening these files via the Rescue Media.

Please ensure that you are actually looking at the correct drive letter for your backups when using the rescue media as the drive letter is often different that what you see in Windows.

One tip here is to create a text file in the root of your USB drive that you can check for when looking at the drives.  Another is to change the volume label for the USB drive so that it stands out as being your backup drive.

One further late thought - your drive shows as being larger than 4TB in size and formatted as GPT, please ensure that you are booting the Rescue Media in UEFI mode, not as a Legacy device which would not support the size of the GPT USB drive.

You should see the letters UEFI next to the USB device in your boot selection panel from the BIOS.

See KB 59877: Acronis True Image 2017: how to distinguish between UEFI and Legacy BIOS boot modes of Acronis Bootable Media for some further information.

I put the text file on the drive as you suggested and booted into the drive using UEFI mode. I went through all the drives but could not see the text file I created nor the backups.

Do you think it's a problem of how the drive is formatted? If you look at the partitions image in my first post and compare Disk 1 (D:) and Disk 3 (Z:), Disk 1 has a GPT (Reserved Partition) along with the data partition, while Disk 3 (where my backups are) just says GPT, and under File System is says unallocated instead of Other.

Solved it. It was a formatting problem. First I moved one of the backups to another drive, then I cleaned the external drive using diskpart, then I reformatted it as a GPT drive and added the partition. Now it shows the Reserved Partition. I booted into the recovery drive and now I can see my backup.

Joe, the partitions information looks fine to me, the key portion of your USB drive is formatted as NTFS on the GPT partition and the 1MB unallocated space is simply a matter of how the partition is aligned on the drive.

At this point I suspect the issue is related to the type of Acronis Rescue Media that you are booting from where this is probably the Linux media (based on the files shown for your USB drive G:).

I would recommend creating the alternative WinPE version of the rescue media which will have greater compatibility with your backup drive.  The files I see on my own WinPE media look as below for the top ones listed.

See KB 60820: Acronis True Image 2018: how to create bootable media

and KB 60091: Acronis True Image 2018: how Simple bootable media creation mode works

Joe, our posts crossed so just seen your last update, glad you have sorted this issue and all is now OK.

Thanks