There are currently two different Lightning to 30-pin adapters offered by Apple. Neither of these adapters will work with the bottom of your Grove case on. They are both larger than the regular Apple Lightning charger.
We are not yet aware of other third-party adapters that will work with the bottom of the case on. However, as long as the Lightning head of the adapter is the same size or smaller than the regular Apple iPhone 5 charging cable, the adapter should work without removing the bottom of the case.