  The inverse Compton scattering of ultrarelativistic electrons accelerated at
the pulsar wind termination shock is believed to be responsible for TeV
gamma-ray signal recently reported from the binary system PSR B1259-63/SS2883.
While this process can explain the energy spectrum of the observed TeV
emission, the detected gamma-ray fluxes do not agree with the published
theoretical predictions of the TeV lightcurve. The main objective of this paper
is to show that the HESS results can be explained, under certain reasonable
assumptions, by inverse Compton scenarios of gamma-ray production in the
system. In this paper we study evolution of the energy spectra of relativistic
electrons under different assumptions about the acceleration and energy-loss
rates of electrons, and the impact of these processes on the lightcurve of IC
gamma-rays. We demonstrate that the observed TeV lightcurve can be explained
(i) by adiabatic losses which dominate over the entire trajectory of the pulsar
with a significant increase towards the periastron, or (ii) by the sub-TeV
cutoffs in the energy spectra of electrons due to the enhanced rate of Compton
losses close to the periastron. The Compton deceleration of the pulsar wind
contributes to the decrease of the nonthermal power released in the accelerated
electrons, and thus to the reduction of the IC and synchrotron components of
radiation close to the periastron. Although this effect alone cannot explain
the observed lightcurves, the Comptonization of the pulsar wind leads to the
formation of gamma-radiation with a line-type energy spectrum. While the HESS
data already constrain the Lorentz factor of the wind, $\Gamma \le 10^6$,
future observations of this object with GLAST should allow a deep probe of the
wind Lorentz factor in the range between $10^4$ and $10^6$.
