A Ghost lives in my website

Hi,

5 days ago I posted a comment to Wordfence support site but nobody replied since than. 2 days ago I deactivated and deleted Wordfence but the strange events are still happening. Probably the problem is related to WordPress. I’d appreciate any feedback if anyone has a clue what could be the reason and how can I get rid of it. Many thanks. Here comes my post:
—
Since I have installed Wordfence strange things happen. Wordfence Live Traffic lists an activity – an attempt to access a particular “non-existent” page – every time I log in to my website. It refers always to the same page, and that page actually exists. If I click on the permalink shown in the Live Traffic item I’m taken to that page with no problem. I can edit it, modify it, just like any other pages on my site.

I have another plugin named Counterize which creates nice statistics directly in my Admin Dashboard and lists all (?) access to my site. If I look at it’s Traffic History I can see another interesting stuff – again since I have installed Wordfence: Every time I log in to my site I can see two, almost simultaneous, visit in my Traffic History. One to my home page with Referer ‘Unknown’, which is OK, that’s what I did. But there is another access shown just few milliseconds after that every time: an access to the same page listed in Wordfence Live Traffic with Referer = Home page. I can’t even click so fast, the difference in the time stamp between them is 5-6 milliseconds.

What’s more, similarly strange, Counterize Traffic History always shows another extra access every time I visit other pages, posts or comments on my site. Regardless where do I go in my site, an additional access seems to happen every time.

I’ve got the impression that either Wordfence (or WordPress ?) planted some sort of code somewhere which is executed every time I access a post. I can send screenshots if it helps to figure out whats going on.