Two-sided matching systems, such as admissions pipelines, allocate opportunities jointly. Reducing a protected at tribute's influence usually requires encoder retraining.

We study a closed-form linear projector that does this at inference time. For markets that stay vertically ordered before and after the edit, we bound the mean welfare change by the edit-induced appeal shift and an explicit remainder.

A probabilistic refinement replaces worst-case constants with a data-dependent deviation term. A pre-deployment screen combines a verticality test with a welfare sweep and returns PASS, KILL, or OUT-OF-SCOPE.

An exact tier requires every opportunity to rank applicants by appeal, and a graded tier admits near-vertical markets. On 30 held-out synthetic markets, the screen agrees with every pre-specified regime verdict, with no observed false PASS.

On 60 exactly vertical markets, no bound is violated, and the probabilistic bound is informative in 69% to 87% of configurations. On 2700 configurations from three realistic markets, which do not reach the exact tier, no plug-in bound expression is violated.

A closed-form factorization stays within graded scope in 90% to 100% of instances, whereas two-tower and graph neural network encoders fall outside it in every instance. Architecture choice thus appears to affect whether a post-hoc edit is admissible.