Entity Matching (EM) is a critical task in numerous fields, such as healthcare, finance, and public administration, as it identifies records that refer to the same entity within or across different databases. EM faces considerable challenges, particularly with false positives and negatives. These are typically addressed by generating matching scores and apply thresholds to balance false positives and negatives in various contexts. However, adjusting these thresholds can affect the fairness of the outcomes, a critical factor that remains largely overlooked in current fair EM research. The existing body of research on fair EM tends to concentrate on static thresholds, neglecting their critical impact on fairness. To address this, we introduce a new approach in EM using recent metrics for evaluating biases in score based binary classification, particularly through the lens of distributional parity. This approach enables the application of various bias metrics like equalized odds, equal opportunity, and demographic parity without depending on threshold settings. Our experiments with leading matching methods reveal potential biases, and by applying a calibration technique for EM scores using Wasserstein barycenters, we not only mitigate these biases but also preserve accuracy across real world datasets. This paper contributes to the field of fairness in data cleaning, especially within EM, which is a central task in data cleaning, by promoting a method for generating matching scores that reduce biases across different thresholds.