When you log into your blogger account,If you load your blogger website in same browser you can see quick editing buttons near your blogger widgets.If you don't like it you can remove it easily.
1.Login to your dashboard--> layout- -> Edit HTML
2.Click on "Expand Widget Templates"
3.Scroll down to where you see this code\codes :
<b:include name='quickedit'/>
4.Now delete this code and save your template.
You are done.Now you can not see below button.
File Under : change template, html