Excuse me, what button??

Mozilla added a square button with an arrow inside pointing down, it's located just left of the 'bookmark this page' star. Cursor pop up says 'add to taskbar' and if actuated, it will add the page in view to the taskbar, however, sometimes when adding tabs or switching to other tabs it generates a drop down dialog box with the message 'add this site' with a silly looking caricature of a Fox, I presume the Mozilla Fox. Hopefully, TyDraniu, I've been succinct enough for you or some other contributor to give instruction on eliminating this bother.

Enter about:config in the address bar and switch browser.taskbarTabs.enabled to false.

Thanks, perfect!