ivanmihalev

It was a problem with WP Simple Galleries plugin, and to be more exact, with the colorbox library file jquery.colorbox-min.js.
This plugin is a little bit outdated (some 8 years ?? ), and because of that jquery.colorbox-min.js stays in its 1.3.4 version. But on Jack Moore web site there an 1.6.4 version is laid. So, I just replaced my outdated file with the new one, and viola, nasty “close” disappeared.
This was a kind of brute force resolving of the problem, but it worked to me.

Thank you for the advice James!

Sorry, I just did not took in account that nginx is used.

Tray to look at the content of .htaccess file. It sits at the root folder of your site or/and the root of your WP installation (the last is just in case if you install WP as subfolder of your web site like /<web root folder>/<WP root subfolder>).
As you may know, in this file are stored some setting and the most important, some rewriting rules. So, it is possible a rule to exist, that rewrites https:// to https:// or vice versa. It is possible too, if this file for some reason is not writable to WP, to be impossible for WP to write inside the right settings and rules.
Just to remind, you may have more than one .htaccess file in your web site (even every folder may have such a file), so you have to find the right one – in the web root or in the WP root (the last is most probable suspect).
This way to resolve your problem is of the kind “the last thing to do”, so be careful if you decide to edit rules by hand.
The usual way is by using the regular WP tools/menus.

Good luck in hunting your bug ??