Thanks. I have done more testing:
I first signed into both ebay.com and amazon.com. In CCleaner, Options, Cookies, I selected all the cookies, right click, "Delete now". I ran CCleaner again, and those cookies no longer showed up.
I then visited ebay.com, and I was still logged into ebay.com (presumably because of cookie). I ran CCleaner again, and ebay.com showed up again.
I then visited amazon.com, and I was still logged into amazon.com (presumably because of cookie). I ran CCleaner again, and www.amazon.com showed up again.
In IE11, Tools, Delete browsing history..., check Cookies, Delete. When I visited ebay.com or amazon.com, I was no longer logged in.
So CCleaner is likely using the APIs to some extent, but is not cleaning cookies completely.
CCleaner still works fine with 1703 to clean IE11 cookies. I have tried both versions 5.37 and 5.38 with 1709.