I’ve been seeing this annoyance frequently of late: “Your phone has been compromised”, or something similar to that. On, sad to say, oann.com, a conservative news site.

Clicking the “X”, the usual “dismiss” symbol, has no good effect. The only way I’ve found to kill the pop-up is to close the page in my Safari browser. Then I have to relaunch oann.com, then reposition it to my preferred location among the other Safari pages. Grrr.

It's their advertisers. You can't do a ton about and the site has limited control as they don't pick individual advertisers.

Stay off those sites and be sure your Apple software/firmware is up to date.
I had that problem a few years ago but not recently so I guess Apple figured out how to stop it, for now.

Try AdBlock. I don't recall if it's free or a paid app, but it eliminated most of the pop up ads on my iPhone.