  Weak-lensing peak counts provide a straightforward way to constrain cosmology
by linking local maxima of the lensing signal to the mass function. Recent
applications to data have already been numerous and fruitful. However, the
importance of understanding and dealing with systematics increases as data
quality reaches an unprecedented level. One of the sources of systematics is
the convergence-shear inversion. This effect, inevitable when carrying out a
convergence field from observations, is usually neglected by theoretical peak
models. Thus, it could have an impact on cosmological results. In this paper,
we study the bias from neglecting (mis-modeling) the inversion. Our tests show
a small but non-negligible bias. The cosmological dependence of this bias seems
to be related to the parameter Sigma_8. When this bias propagates to the
parameter estimation, we discovered that constraint contours involving the dark
energy equation of state can differ by 2-sigma. Such an effect can be even
larger for future high-precision surveys and we argue that the inversion should
be properly modeled for theoretical peak models.
