The satellite gravity gradiometry (SGG) data can be used for local modelling of the Earth's gravity field. In this study, the SGG data in the local north-oriented and orbital frames are inverted to the gravity anomaly at sea level using the second-order partial derivatives of the extended Stokes formula. The emphasis is on the spatial truncation error and the kernel behaviour of the integral formulas in the aforementioned frames. The paper will show that only the diagonal elements of gravitational tensor at satellite level are suitable for recovering the gravity anomaly at sea level. Numerical studies show that the gravity anomaly can be recovered in Fennoscandia with an accuracy of about 6 mGal directly from on-orbit SGG data.