I thank you for trying to help, but it didn't. "Simply select the CCleaner icon again". What icon? The CCleaner program shortcut on my desktop is the only CCleaner icon i can find. But if i click on it [obviously enough] all that happens is that i now have two copies of Ccleaner open at once. That and i find the same old undeleted list of cookies.
You misread my reply, which was made carrying on from the position you were at in you post, and that is with CCleaner open and looking at the "Cookies To Delete" window.
From the position you are at in your post, go to the Cleaner icon as shown here:
And then select "Run CCleaner" as depicted here:
You may have been mislead by my typo of using double C for the icon when it should have been the single C spelling. My apologies if that was the case.
Frustated, i rechecked my CCleaner Applications check list. I was using Opera, so left Firefox cookies unchecked. In a why-not mood, i checked Firefox. And then used Firefox to see if it was retaining the same sites cookies. Success!
My extraneous Firefox cookies are now vaporized.
My Opera cookies remain indestructible but I'm jumping ship to Firefox anyway, so i'm content with not solving that mystery. [Opera users: your cntrl+shift+L bulk downloads, Opera's clumsy equivalent of Firefox's Downthemall, may lose files. Mine does, an obviously fatal bug.]