what is the strange search icon that shows up on a webpage in Safari iOS on iPhone

There is at least one website that when I go to it, an icon that looks like a white magnifying glass inside a black circle appears. I've attached 3 screenshots to illustrate. The second one is with using the "reader view". The third one is when I click on the icon in pic #2 (very similar to when I click on the icon in pic #1).

I've Googled it and can find no way to identity where it's coming from or how to turn it off. It "may" be that it's strictly related to this website: thundercloud.net/infoave/new/s6595-2. It's a website that contains info on Windows and they have a "daily" page and a "weekly" page - also know as "Cloudeight infoave".

I'm using an iPhone 8 running iOS 16.6 using the Safari browser. It's not a major problem for me since other websites don't appear to experience this - but it is a distraction. If someone knows what this is all about and how to turn it off, please let me know.

BTW, I already looked under Settings>Safari>Quick Website Search and that is toggled "Off" with no websites listed underneath it.

Thank you.

-Marty

P.S. - Sorry for not downsizing these pics.