BBB wouldn't do anything anyway. The shop would only be obligated to "repair" the product again. But lets be honest, you don't want to go back.
I went through BBB when I had my transmission rebuilt for the prelude and found that, while R synched fine, 2nd and 3rd had issues in cold start up. And my brake reservoir cap was loosened. Absolutely no explanation on their part for this. BBB felt it was adequate that the shop offered to "look at it again", but I refused, for my own safety, to not let them touch my car.