  We study the dynamics of a hierarchical three-body system in the
general-relativistic regime: an extreme mass-ratio inner binary under the tidal
influence of an external body. The inner binary consists of a central
Schwarzschild black hole and a compact test body moving around it (outer
binary). We discover three types of tidal effects on the orbit of the test
body. First, the angular moment of the inner binary precesses around the
angular momentum of the outer binary. Second, the tidal field drives a
"transient resonance" when the radial and azimuthal frequencies are
commensurate with each other. In contrast with resonances driven by the
gravitational self-force, this tidal-driven resonance may boost the orbital
angular momentum. Finally, as an orbit-dynamical effect during the non-resonant
phase, we calculate the correction to the Innermost Stable Circular (mean)
Orbit (ISCO) due to the tidal interaction. Hierarchical three-body systems are
potential sources for future space-based gravitational wave missions and the
tidal effects that we find could contribute significantly to their waveform.
