I tried:
The settings for the Visual Studio Git Extensions toolbar can be found in this file:
\Users{username}\Documents\Visual Studio 2012\Settings\CurrentSettings.vssettings
Search the file for the term GitExtensions to find the toolbar setting lines. There will likely be two lines, not necessarily next to each other:
You'll want to modify the second of the two lines, since it will take precedence, and it already has the settings in it.
You can set the Visibility to "auto" to make it behave like other toolbars, or "hide" to just get rid of it. Set the Row to 1 if you want it to stick to the first row of toolbars.
Of course you'll have to do this with VS closed in order for it to work properly.