You can. :)
To clear your current path:
In the activity tracker, right-click/long-press and Remove your current path
or
In the achievement path window, press the Clear Path button at the bottom
(Is it specifically Turael's Burthorpe paths you want to get rid of? When you clear your path, if you haven't completed Turael's Burthorpe paths, that button will be re-labeled Skip Tutorial, which you can press to flag them as complete)
If you need to re-open them, you should have a button for both activity tracker and achievement paths on your bottom-right ribbon.
Alternatively, the achievement paths window is on your achievement screen. (Press F1 (or Esc and choose Hero), then the Achievements tab). You can drag and drop the window out from there.