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 Σ8 ≡ (Ωm∕(1 − α))1 − α(σ8∕α)α, where α = 2∕3. When this bias propagates to the parameter estimation, we discovered that constraint contours involving the dark energy equation of state can differ by 2σ. 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.Key words: gravitational lensing: weak / large-scale structure of Universe / methods: numerical