Measuring the carbon footprint of economic sectors is essential for assessing climate-related risks, especially for financial institutions. This paper estimates Uruguay's sectoral carbon footprint using an Environmental Input-Output (EIO) approach, focusing on the banking sector. By linking emissions to bank loan portfolios, we examine how credit allocation affects financial institutions' carbon exposure. The results show that indirect emissions reshape sectoral rankings, emphasizing the need to look beyond direct emissions. The banking sector's adjusted carbon footprint has risen over time, driven by sectoral emissions growth and changes in credit-to-output ratios. However, variations among banks highlight the role of credit allocation. Limitations include data aggregation, reliance on historical input-output data, and the inability to distinguish between loans for high-emission activities and green investments. The findings stress the need for better tools to assess financial sector climate risks.