Understanding the mechanisms that limit the current transport in granular iron-based superconductors is necessary to unlock their potential for magnet applications. This paper reports the transport critical current surface IC(T,H) of powder-in-tube Ag/Ba1−xKxFe2As2 tapes densified by flat rolling and uniaxial hot pressing. We investigate the amplitude of the isothermal-IC(H)-curve magnetic hysteresis, which is a marker for the electrical connectivity between superconducting grains. This allows us to demonstrate that, in spite of an improved connectivity, the percolative path through weakly linked grains continues to play a role in the IC properties of hot-pressed conductors. The limitations to the current transport due to weak links depend on the orientation of the magnetic field and are more severe when H is on the tape plane. This finding provides a justification to the puzzling evidence that IC (H) can be smaller for magnetic fields applied on the tape plane and not perpendicular to it. Finally, we report an unexpected increase of IC upon augmenting the magnetic field from 0 to ~2 T. SQUID measurements reveal a superparamagnetic-like magnetic background that takes place in the same range of magnetic fields. A microscopic study of the conductor-core elemental composition provides evidences that these features can be both related to the presence of Fe-rich non-stoichiometric regions in the superconducting core. On a more general note, this study points out that further advances in the in-field current transport properties of powder-in-tube Ag/Ba1−xKxFe2As2 conductors are possible and rely to a large extent on solutions to improve the inter-grain connectivity and the quality of the superconducting phase.