I assume that you are backing up to a Time Capsule, correct?
Disconnect the G Drive from your Mac to simulate a situation where the drive has failed, and you need to get at the data on the drive on your Time Machine Backup.
Open Time Machine on your Mac and give it a few minutes to fully load
Using the timeline on the right of Time Machine window, go back a few days in the past to select a date
Look on the left side of the Finder window in Time Machine for a heading called Devices
Click on the name of your Mac computer under the Devices heading
The window to the right should display two folders, each representing a hard drive that has been backed up
The backups of your Mac are in a folder called Data.....(unless you have changed the name of the drive on the Time Capsule)
The other folder should display the name of the G Drive
Right-Click on the G Drive and a drop down menu will appear
Click Restore To to select a destination where the entire backup of the G Drive will go
If you don't want to restore the entire G Drive, open up the drive in Time Machine and navigate to find the file or folders that you need
Then, click to select and highlight the folder(s) and then Right-Click to display the Restore To option