A re-usable rocket can launch to match altitude and speed with the bottom of the tether which is in a non-keplerian orbit (travelling much slower than typical orbital speed). The payload is transferred and it climbs the cable. The cable itself is kept from de-orbiting via electric propulsion and/or electromagnetic effects.
A reusable rocket can reach the same altitude and speed as the tether at the bottom of its non-Keplerian orbit, which travels much slower than typical orbital speeds. The payload is transferred to the cable, which is kept from deorbiting using electric propulsion and/or electromagnetic forces.