Traffic redundancy elimination (RE) is an attractive approach to improve the throughput in bandwidth-limited networks. While previous studies show that the RE is useful for improving the throughput in such networks, we observed that the RE would not be an effective solution in wireless networks. We found the TCP congestion control cannot take advantage of the RE, without knowing how the underlying RE system manipulates each TCP packet. In this letter, we present a novel technique called REboost to enable the TCP layer to be aware of the underlying RE system and improve the throughput. Our evaluation with a prototype shows that REboost significantly improves the throughput compared with the previous RE systems.