Some PDF files (like those generated by Acrobat when using the Compare Documents command) have locked comments that can't be edited or removed. You can use this simple (and FREE) script to unlock all of these comments with a single click, and then you'll be able to edit them, unless there's a security policy that prevents it.

This script can be used in both Adobe Acrobat and Adobe Reader.
You can download it here.

Here's how it looks like in Reader:

The original file with the locked comments. Notice the padlock icon next to each one on the right.

The same file after running the script on it from its menu item in the Tools panel.

The resulting file. All the padlock icons are gone, and I was able to delete the first highlight on the page.