External HD shows "Invalid Extent Entry" in Disk Utility First Aid for the Time Machine "Backup" volume. Erase that Backup volume?
The invalid extent entry error basically means the directory on your drive is corrupted. In other words the index of what files are stored and where they're stored is all mucked up. 

This can be repaired but not without risk. You basically have two options if you still want to keep using this drive:


Use a third party disk utility that can repair the corrupted directory (e.g. DiskWarrior, Techtool Pro, etc)
Reformat the partition 


Note: I have no affiliation whatsoever with either DiskWarrior or Techtool Pro.

Regardless of the option you choose I would still recommend manually backing up any files you can still access to another drive. Obviously this is a must do if you opt for the second option.

As to your concern about accidentally reformatting the other partitions, this shouldn't be a problem as long as you're only selecting the particular partition (or volume) with the error.

More specifically:


launch Disk Utility 
select the partition in the sidebar 
click the erase tab
make sure the format in the drop-down menu is the one you want 
give it a name 
click on Erase