It's strange but I found another line which created the artifacts, and this line used the FLTK GUI. Namely, at the end of the callback for the startButton I used the following line:
startButton->deactivate();

(the startButton is of type Fl_Button)

When I commented out this line, evertything started to work correctly, no artifacts. So I moved this line before following line:
addMessage(gui.getTranslation().Translate(u8"Connected!").c_str());

So now the code looks like this:
startButton->deactivate();
addMessage(gui.getTranslation().Translate(u8"Connected!").c_str());

Now there are no artifacts at all. The addMessage() method is following:
void GUIDlgNetClient::addMessage(std::string msg)
{
    netMessages->insert(msg.c_str());
    netMessages->insert(u8"\n");
    Fl::check();
}
The netMessages is definied like this:
using FlMultilineOutputPtr = std::unique_ptr<Fl_Multiline_Output>;
FlMultilineOutputPtr netMessages;

Seems there is a strange coincidence between the Fl_Multiline_Output (netMessages) and the Fl_Button (startButton). If I write something to Fl_Multiline_Output, and then disable the button, I get the artifacts. When I first disable the button and then write to Fl_Multiline_Output, everything is OK.