Those icons come from the Brackets Interactive Linter extension, created by the same author. However, they don't give you "auto correct" options like the lightbulbs in some other editors. As far as I can tell, the icon just shows you more details about the linting error.
If "auto correct" is what you're looking for, you might still be able to interest someone in working on that functionality. (The Brackets community is pretty responsive!). I suggest:
- File an issue in the extension's repo asking for the enhancement; or
- Start a thread on the brackets-dev forum making this suggestion, in case any other extension developers would be interested in working on it.