Hi Robert - there is no need to worry, nobody can delete or change your route. Clicking EDIT only allows them to edit the map but not save changes (apart from saving a copy to their own account).
I put your map on my website. It looks more than awesome!
But one thing: even if I created this map everybody are able to click "menu" icon (right up corner) then edit and change or celar my map! It is possible to diable this option to prevent from deleating my route?