In online advertising under the cost-per-conversion (CPA) model, accurate conversion rate (CVR) prediction is crucial. A major challenge is delayed feedback, where conversions may occur long after user interactions, leading to incomplete recent data and biased model training. Existing solutions partially mitigate this issue but often rely on auxiliary models, making them computationally inefficient and less adaptive to user interest shifts. We propose IF-DFM, an Influence Function-empowered for Delayed Feedback Modeling which estimates the impact of newly arrived and delayed conversions on model parameters, enabling efficient updates without full retraining. By reformulating the inverse Hessian-vector-product as an optimization problem, IF-DFM achieves a favorable trade-off between scalability and effectiveness. Experiments on benchmark datasets show that IF-DFM outperforms prior methods in both accuracy and adaptability.