Now you can choose to hide or display the quick editing tool by going into Blogger edit post options but do read aboutwhy you should keep the quick editing tool before you remove them.
(If you only want to know how to permanently get rid of those quick editing icons, skip to Permanently get rid of pencil icon orPermanently get rid of screwdriver/wrench icon but I hope you will read the explanation on why you should not remove those useful icons)
<b:include name='quickedit'/>
If you face difficulties finding that line of code, press ctrl+F and you will see a "Find" followed by a box for you to type or copy-paste what you want to find. Type or copy-paste the above line of code into the box and click "Next". The scroll bar will scroll down to the line and the line will be highlighted. Use your mouse to highlight that line of code again and press the DELETE key. Preview, and if you don't get any error message, click "Save Template". You will never see the "irritating" (to me, useful") screwdriver and wrench icons again.
Update: 25 May 2010: A commentator Susie Hovendick Chan said that she got rid of the quick edit icons by putting
quickedit:display none;
at the end of the style sheet, that is, just before ]]> thus ending with
quickedit:display none;
]]>
(If you only want to know how to permanently get rid of those quick editing icons, skip to Permanently get rid of pencil icon orPermanently get rid of screwdriver/wrench icon but I hope you will read the explanation on why you should not remove those useful icons)
We have received numerous complaints of bloggers seeing those "irritating" quick editing icons - the pencil 
quick edit icon for the posts, and the screwdriver and wrench (spanner) 
quick editing icon for the Page Elements (widgets). Personally they don't irritate me at all.
To me, these are really useful features, especially if you put a lot of HTML/Javascript Page Elements and you don't type a title for the Page Element (which is the norm). In the LAYOUT, they will all read "HTML/Javascript" and there is no way for you to tell which HTML/Javascript is for what unless you click on EDIT to look at what is inside. On the other hand, if you are logged in and you go the the blog, you will know exactly which Page Element you want to edit/delete and all you have to do is to click the icon and you will be editing/deleting the Page Element you want to edit/delete.
Further, they are only visible to me when I am logged into Blogger. No one else will see it. I have written about it before atHow to get rid of the irritating "pencil" and "screwdriver and wrench (spanner)" quick edit icons (click BACK button to get back to this page). This however don't seem to satisfy some bloggers, especially those who have private blogs and can view their blogs only when they are logged in.
Here is one comment from a particularly irritated blogger:
"Okay 300 ducats to cooked art, his method worked. The other anwers are basically saying, 'Don't worry -- nobody who uses your blog will see these eyesores but you.' Which seems like an odd thing to tell me, since I will be using my blog more than anyone else, and I don't actually enjoy looking at eyesores any more than they would."
OK, if getting rid permanently of those very useful quick edit icons is what you want, here is how you can do it:
quick edit icon for the posts, and the screwdriver and wrench (spanner) 
quick editing icon for the Page Elements (widgets). Personally they don't irritate me at all.To me, these are really useful features, especially if you put a lot of HTML/Javascript Page Elements and you don't type a title for the Page Element (which is the norm). In the LAYOUT, they will all read "HTML/Javascript" and there is no way for you to tell which HTML/Javascript is for what unless you click on EDIT to look at what is inside. On the other hand, if you are logged in and you go the the blog, you will know exactly which Page Element you want to edit/delete and all you have to do is to click the
icon and you will be editing/deleting the Page Element you want to edit/delete.Further, they are only visible to me when I am logged into Blogger. No one else will see it. I have written about it before atHow to get rid of the irritating "pencil" and "screwdriver and wrench (spanner)" quick edit icons (click BACK button to get back to this page). This however don't seem to satisfy some bloggers, especially those who have private blogs and can view their blogs only when they are logged in.
Here is one comment from a particularly irritated blogger:
"Okay 300 ducats to cooked art, his method worked. The other anwers are basically saying, 'Don't worry -- nobody who uses your blog will see these eyesores but you.' Which seems like an odd thing to tell me, since I will be using my blog more than anyone else, and I don't actually enjoy looking at eyesores any more than they would."
PERMANENTLY GET RID OF QUICK EDITING PENCIL ICON FOR POSTS
Sign into Blogger (Dashboard), click SETTINGS for the relevant blog and you will be in the SETTINGS > BASIC sub-tab by default. Just a bit down from the top of the page, you will see "Show Quick Editing on your Blog?". Click the down arrow and select "No" At the bottom, click "Save Settings". (Warning: There is a button "Delete this blog" very near that "Save Settings" button, and it is not uncommon to hear of bloggers who accidentally deleted their blog this way). Once you have done that, you will never see the quick editing Pencil icon again.PERMANENTLY GET RID OF QUICK EDIT SCREWDRIVER AND WRENCH (SPANNER) ICONS FOR PAGE ELEMENTS (WIDGETS)
Sign into Blogger (Dashboard). Click LAYOUT for the relevant blog. Click TEMPLATE tab, followed by EDIT HTML sub-tab. Before you do any editing of the template, backup the template PLUS the Page Elements. See Backup and edit New Blogger template PLUS backup Page Elements. Once you are done with that, you will still be in the template editor window. Tick the "Expand widget templates" box and wait for the template to fully expand. Then look for this line of code:<b:include name='quickedit'/>
If you face difficulties finding that line of code, press ctrl+F and you will see a "Find" followed by a box for you to type or copy-paste what you want to find. Type or copy-paste the above line of code into the box and click "Next". The scroll bar will scroll down to the line and the line will be highlighted. Use your mouse to highlight that line of code again and press the DELETE key. Preview, and if you don't get any error message, click "Save Template". You will never see the "irritating" (to me, useful") screwdriver and wrench icons again.
Update: 25 May 2010: A commentator Susie Hovendick Chan said that she got rid of the quick edit icons by putting
quickedit:display none;
at the end of the style sheet, that is, just before ]]> thus ending with
quickedit:display none;
]]>