Found this when testing opera with a site I'm working. Hated it immediately.
Here's some css to hide it:
body + div[is-visible] {
display: none !important;
}
Edit:
Some more details.
Firstly, this is was done with reference to Opera 39 on desktop. Other versions may be slightly different but hopefully this has enough information that someone else can help come up with a solution that works in them too.
I found the button is attached to the document in a div at the bottom of the page (directly after the body element). You can see it in the browser using the page inspector.
The button itself seems to be part of the DOM so there's no way to apply css to it directly, so I've had to get about that by hiding it's container (the div).
The is-visible attribute is only really there to keep from confusing it with other elements. Best I can tell that attribute is only used in Opera.