Access to MacBook Air backup files
If you are an administrator (i.e. have an admin account) on the MacBook Air and are familiar with the command line interface you can use the sudo command to obtain machine-level admin rights. Once you have those rights, you can access the files in that folder.

An example of this might be:

$ cd ~/Desktop
$ mkdir luannsphotos
$ sudo cp -R G-Drive/Backups/LuAnne'sMacBookAir/Latest/MacintoshHD/Users/luanne/Pictures/* luannsphotos


This is pseudo-"code", but essentially I've created a folder in your home folder, and then recursively copied the contents of that folder you referenced into this new folder.