In Hill’s mechanism, the gravitational tidal force of a single MBH disrupts an approaching binary. One star is captured on an eccentric orbit around the MBH and, by conservation of energy, the other star escapes with a final velocity equal to the geometric mean of the ∼$10^4$ km/s infall velocity and the ∼$10^2$ km/s binary orbital velocity.
Hypervelocity Stars and the Galactic Center, Warren R. Brown, p.3
I don't understand how the high energy/velocity can be transferred to the star.
(Hills' 1988 Nature paper is still paywalled.)