<p>Calibration of option pricing models is routinely repeated as market quotes, filters, and data sources evolve. In standard practice, if a subset of quotes is later excluded because of stale observations, vendor corrections, revised liquidity filters, or audit restrictions, the retained-data calibration problem is typically rebuilt and resolved. This paper studies a complementary question: when a Gauss–Newton calibration system has already been constructed, whether the numerical influence of selected quotes be removed without reconstructing all quote-level pricing and sensitivity evaluations. Therefore we formulate selective forgetting for parametric option calibration as an operator acting on Gauss–Newton sufficient statistics. At a fixed reference linearization, quote-level residual and Jacobian contributions enter additively, which permits exact deletion and shard-local recomputation operators. We derive stability and perturbation bounds for the resulting parameter update and clarify the limitations of the approach beyond the fixed-linearization regime. Numerical experiments with Heston-type calibration illustrate that the proposed operators reproduce the retained-data Gauss–Newton update while reducing recomputation in repeated deletion and sensitivity-analysis scenarios. The method provides a first operator-theoretic foundation for post-calibration deletion, audit correction, and influence analysis in derivative calibration workflows.</p>