Last week, I wrote about adding the +1 button. When added, it adjoins the other 'Share' buttons feature. Once selected, it can't be removed in the Blog Post Page Element. Of course, you can hide it, or make it non-functional, by un-checking the box next to it, but you can't remove it there.
Some people like the +1 concept, and some don't. However, as easy as it is to add +1, it is difficult to remove it. You will have to remove some script from your template - and tweaking your template is always fraught with dangers, if you are not careful.
You will need to navigate to your Design Screen, then click on Edit HTML.
The first thing you MUST do, is to make a Back-up copy of your Template. That's the first option on the Edit HTML screen. If you don't know how, read this post.
Once you have secured your Back-up copy, check the Expand Widgets box.
Scroll down through the template script to find this piece of code, and remove it:
<div class='goog-inline-block dummy-container'><data:post.dummyTag/></div>
Once removed, you have to click 'Save Template'. Then, as a precaution, once again, make another Back-up copy of your Template.
Once this is done, the +1 feature/button should be gone from your Share Buttons.