To promote sustainable development, manufacturers must effectively reduce their carbon emissions. However, doing so often incurs higher costs for carbon emission reduction (CER), which can worsen the capital-constrained problems faced by manufacturers operating within a retailer-led supply chain. To address this challenge and optimize CER efficiency within limited funds, we propose a two-echelon supply chain model led by a retailer. We then analyze six different scenarios, including no financing, bank loan financing and retailer credit financing, both with and without CER investment, to identify optimal strategies for each situation. The results show that: (1) Increasing interest rates on bank loans and retailer credit will have a negative impact on the CER efficiency and retailer's profits. (2) If the initial funds are below a certain threshold, a higher interest rate on bank loans will reduce the manufacturer's profits. However, as the initial funds increase, a higher interest rate can improve the manufacturer's profits with the retailer's credit financing strategy. (3) The manufacturer's optimal financing strategy depends on both the interest rates and initial funds, while the retailer's credit decision is solely based on the manufacturer's initial funds. (4) The retailer credit financing strategy can lead to a mutually beneficial outcome by adjusting the interest rate of the retailer credit, thereby improving the CER efficiency and relieving financial pressure. However, the bank loan financing strategy does not have this advantage.