The badass tokens are stored on your profile. 360 profiles are just large container files, just like regular save files, and the files inside the profile are GPD files.
Modding GPD files is a lot like modding any other save. First you have to extract them from the profile. They're numbered, not titled, so you need to know which number corresponds to which game. Most GPD editors will tell you which number to extract. Next you have to do the modding, and that's the same as with a typical save. After that, reinject the GPD, rehash/resign, and load your profile back into your HDD.
The biggest risk with GPD modding is that you can potentially corrupt your profile. Also, because each profile is loaded into Microsoft's servers for recovery, you will likely never be able to "unmod" your GPD. Add to that, it's somewhat (not by much, but somewhat) easier to get banned via GPD modding, usually when achievements are involved.
I say go for it for this game. I did, and it's nice to have a 400% power boost in tight spots. However, a friend of mine modded his tokens above 2 billion and now he crashes any game he's in and can't "unmod" it. So if you do decide to mod it, use sense about it.
Either way, Gibbed's editor doesn't mod the GPD, so if you do decide to mod it you will need to hunt down a GPD editor somewhere.