Almost all files are locked in my Time Machine backups?
Go to Disk Utility, select the partition of your drive with the Time Machine icon, and click Repair Disk to verify and fix any problems with permissions settings (see below image).  

You may also want to repeat the process with Macintosh HD to be safe.



update Is this option checked for you? If not, it should be unchecked and Saved (from OSX Daily)