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Past planetary missions have been broad and detailed for Gas Giants, compared to flyby missions for Ice Giants. Presently, a mission to Neptune using electrodynamic tethers is under consideration due to the ability of tethers to provide free propulsion and power for orbital insertion as well as additional exploratory maneuvering --- providing more mission capability than a standard orbiter mission. Tether operation depends on plasma density and magnetic field $\mathbf{B}$, though tethers can deal with ill-defined density profiles, with the anodic segment self-adjusting to accommodate densities. Planetary magnetic fields are due to currents in some small volume inside the planet, magnetic-moment vector, and typically a dipole law approximation --- which describes the field outside. When compared with Saturn and Jupiter, the Neptunian magnetic structure is significantly more complex: the dipole is located below the equatorial plane, is highly offset from the planet center, and at large tilt with its rotation axis. Lorentz-drag work decreases quickly with distance, thus requiring spacecraft periapsis at capture close to the planet and allowing the large offset to make capture efficiency (spacecraft-to-tether mass ratio) well above a no-offset case. The S/C might optimally reach periapsis when crossing the meridian plane of the dipole, with the S/C facing it; this convenient synchronism is eased by Neptune rotating little during capture. Calculations yield maximum efficiency of approximately 12, whereas a $10^{\circ}$ meridian error would reduce efficiency by about 6%. Efficiency results suggest new calculations should be made to fully include Neptunian rotation and consider detailed dipole and quadrupole corrections.