All I can see in your screenshot is the shortcuts, consisting of pinned and frequently visited links. Turning off the actual history would be turning off Settings – Homepage – Recently visited.

These are taken from history, if I delete them in history, then they disappear here. I have turned off the recently visited, so it's not this.

Ah, okay, I didn't phrase that very well, sorry. Shortcuts is basically a history feature too, just not the most recently but the most frequently used addresses. You can pin items, so that they will stay even if you don't visit them as often as before, but there's no option to show only pinned ones. What you can try is pin enough items so that no non-pinned ones will be shown.

Well, there are showing the last visited, once, not frequently. I literally remove 10 last visited in history and they're disappearing here. So, it looks like nothing can be done here... Thanks for your response :)