The geodesic that these photons travel on would lead back to the spacecraft, imparting the gained kinetic energy upon a solar sail, causing acceleration.
[1][2] The spacecraft employing the halo drive is not required to carry fuel, as the photons can be provided from another source.
[3] It is similar in concept to a gravitational assist, though it differs in that a spacecraft employing a halo drive would not physically be travelling around a black hole.
[1] In operating a halo drive, the photons take energy away from the black hole binary, causing the orbit to become more eccentric.
If black hole mergers occur more often than would be typically expected, then it could be a sign of another civilization using a halo drive.