Search Bar Shows Up Briefly – One Time

I’ve got a weird issue. My intention is to remove the search bar – and mostly I’ve accomplished that – accept for (what I currently believe) is a first time visit to my front page. That is, the search bar briefly shows up – then it is gone once navigating the site or refreshing the browser.

Symptoms: the search-bar is located on the upper right – and originally appeared on every page before removing the widget. And, although the search bar is mostly gone it seems to be showing up when first visiting my site – despite being as careful as I can to clear all data/cache/cookies. I have tested using different machines and different browsers.

remedy 1: Using Appearance —> Customize —> Additional CSS and then adding the following did not work.

.site-search {
  display: none;
}

remedy 2: Next, I removed the widget using: Appearance —> Customize —> Widgets —> Main Sidebar

At first remedy 2 seemed to have removed the unwanted search bar. Then, after testing a bit with different browsers and other computers it seems that the search bar briefly shows up upon first visit. Refreshing the browser will remove the search bar – until you clear data/cache/cookies then the search bar is back for a moment when first visiting the page. I can repeat this on a Windows 10 machine using Edge and also on a Linux machine using Firefox.

So, I suppose my first question should be. Can anyone else duplicate what I’m talking about? (see link)

And, if so, then what other things should I try?

Thanks for your help.

The page I need help with: [log in to see the link]