  Relativistic magnetic reconnection is a powerful agent through which magnetic
energy can be tapped in astrophysics, energizing particles that then produce
observed radiation. In some systems, the highest energy photons come from
particles Comptonizing an ambient radiation bath supplied by an external
source. If the emitting particle energies are high enough, this inverse Compton
(IC) scattering enters the Klein-Nishina regime, which differs from the
low-energy Thomson IC limit in two significant ways. First, radiative losses
become inherently discrete, with particles delivering an order-unity fraction
of their energies to single photons. Second, Comptonized photons may
pair-produce with the ambient radiation, opening up another channel for
radiative feedback on magnetic reconnection. We analytically study externally
illuminated highly magnetized reconnecting systems for which both of these
effects are important. We identify a universal (initial
magnetization-independent) quasi-steady state in which gamma-rays emitted from
the reconnection layer are absorbed in the upstream region, and the resulting
hot pairs dominate the energy density of the inflow plasma. However, a true
pair cascade is unlikely, and the number density of created pairs remains
subdominant to that of the original plasma for a wide parameter range. Future
particle-in-cell simulation studies may test various aspects. Pair-regulated
Klein-Nishina reconnection may explain steep spectra (quiescent and flaring)
from flat-spectrum radio quasars and black hole accretion disc coronae.
