You should be able to repair the Carbon Fiber with carbon without issue. It is the exact same technique as you would do with Fiberglass. The only difference is you would likely be using an epoxy compared to a resin like the FG would be using.
The only issue with doing a repair is the strength/durability issue if you do not vacuum bag the part (which you could do, but it doesn't sound to be a strength integral part so no worries if you don't). Make sure the part is super clean when adding the new CF and wear all your protective equipment (organics level mask, gloves, etc.).
I would offer you up some CF cloth, but I'm not even sure I have any left in the shop that isn't already spoken for on projects.