The yellow one is our current logo. It's based on a warning sign, a "git branch" (https://git-scm.com/downloads/logos) and the coala (also attached), which is the logo of an open source project also started by us. We got bad feedback, especially that it looks like a warning sign and scares people.
It was a quick draft, the future logo does not have to have an association to the coala. GitMate.io is not coala. The focus must not be on the coala. An association to the "git branch" would be nice, but isn't necessary. The most important association is Git*Mate*. Emphasizing the Mate, like a helpful coworker, helping you out with your code.
Our tool is used as a plugin on platforms like GitHub. The future logo has to integrate well with those platforms (see screenshots) and has to work as a favicon, i.e. small square sizes have to work well.
Since the logos on GitHub and the favicons are quite small, it's impossible to use text within the logo.
With all those suggestions given, we’re very happy to see better ideas which are not originated in our heads :)