This paper investigates how incorporating carbon emission concerns into monetary policy can influence key macroeconomic outcomes such as output, trade, and welfare. By integrating an atmospheric carbon term into the canonical Taylor rule within a New Keynesian DSGE framework, the study explores the challenge of maintaining economic stability while mitigating carbon emissions. Counterfactual simulations reveal the existence of a policy trap: when central bank exceeds a certain threshold of emission concern, the economy faces persistent declines in GDP, adverse effects on trade dynamics, and enduring welfare losses. The findings underscore the importance of carefully balancing environmental objectives with macroeconomic performance, offering policymakers a nuanced perspective on the trade-offs inherent in emission-concerned monetary policies.