I have this problem on Safari for "The Weather Channel". I tried the two sugggestions:
1) Settings - Safari - Clear History and Website Data, and
2) Settings - Privacy - Advertising - Reset Advertising Identifier ...
I still get the unwanted pop-up.
The link suggested by rbrylawski on Jan 4, 2018 7:20 AM is general and does not address eliminating this unwanted pop-up.
I never use the "X" out in the pop-up. I always back out by using the Safari multi-window icon and then "X" out the whole Safari window and swipe out of Safari.
Thinking that it may have swiped my bookmark, I even tried entering "The Weather Channel" without using my bookmarks.
I do not have the Amazon app - and the suggestion by one iPhone user to delete the Amazon app would not apply.
Despite all these efforts, the pop-up appears every time I go into the weather channel.
Any help would be appreciated.