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Curb space is one of the busiest areas in urban road networks. Especially in recent years, the rapid increase of ride-hailing trips and commercial deliveries has induced massive pick-ups/drop-offs (PUDOs), which occupy the limited curb space that was designed and built decades ago. These PUDOs could jam curbside utilization and disturb the mainline traffic flow, evidently leading to significant negative societal externalities. However, there is a lack of an analytical framework that rigorously quantifies and mitigates the congestion effect of PUDOs in the system view, particularly with little data support and involvement of confounding effects. To bridge this research gap, this paper develops a rigorous causal inference approach to estimate the congestion effect of PUDOs on general regional networks. A causal graph is set to represent the spatio-temporal relationship between PUDOs and traffic speed, and a double and separated machine learning (DSML) method is proposed to quantify how PUDOs affect traffic congestion. Additionally, a re-routing formulation is developed and solved to encourage passenger walking and traffic flow re-routing to achieve system optimization. Numerical experiments are conducted using real-world data in the Manhattan area. On average, 100 additional units of PUDOs in a region could reduce the traffic speed by 3.70 and 4.54 mph on weekdays and weekends, respectively. Re-routing trips with PUDOs on curb space could respectively reduce the system-wide total travel time by 2.44% and 2.12% in Midtown and Central Park on weekdays. Sensitivity analysis is also conducted to demonstrate the effectiveness and robustness of the proposed framework.