And it GZips better as well (4793 -> 2120).
I opened it in Inkscape, converted the text to path. Then ran it through SVGCleaner.
You can also do manual simplification in Inkscape (Ctrl + L) till the quality starts to degrade. This lets you reduce things even further:
3516 bytes, 1726 GZipped.
Also, merging path elements together helps.
For example, here's the logo in 1952 bytes: http://pastebin.com/YYBpWsDE
And I'm sure there's further room for manual reduction, maybe by switching between strokes/fills and further cleaning up the paths.
(It would be cool if someone were to work on an automated system for doing this kind of simplification. But I have a feeling that it's difficult find a general technique that will work across SVG hierarchies, like scaled/rotated groups, etc.)
(If you want, you can also submit a patch in https://github.com/badges/shields.)