Thanks for the reply. That's good to know.
Now, an update to El Capitan came out about 2 weeks ago. You can get the OS 10.11.3 Combo Updater from here:
https://support.apple.com/kb/DL1859?locale=en_US
Also, OS 10.11.4 is in the somewhat "advanced" stages of beta testing, so that update could be released shortly.
Again, I do not know if this is a permissions issue or not, and also I have no experience with Time Machine backups. There is an excellent, venerable, and well reviewed freeware program called Onyx that has quite a few useful features. You can get it from here:
http://www.titanium.free.fr/onyx.html
Make sure you get version 3.1.4 (the first one on that list), as it specifically works with El Capitan. It does have a Repair Permissions feature, but I don't think it will do that for the Time Machine backups you have. That would only apply to your main. "boot" (ie, where the OS is) partition on your internal drive.
There is one possibility that might resolve the issue, but it would involve some work, effort, and using another backup solution. But, someone else who has experience with Time Machine might offer a solution. So, I'll hold off with that, for now.
One other thing you might want to consider is investing in a more advanced Disk Maintenance/Repair program than Disk Utility. Two of the best are TechTool Pro and Disk Warrior. I have both of them (along with Onyx), and I run TechTool Pro once a week for disk cleanup/maintenance on both of my Macs (they have SSDs in each one). It definitely helps in keeping both of my Macs "lean and clean". And, that also includes the backups I make with SuperDuper!. TechTool Pro is less expensive, and it has some more features, but I have read that Disk Warrior can, at times, do "magic" things that other software cannot do.