Sustainable Supply Chain Management (SSCM) aims to address all environmental, social, and economic issues at different levels of the supply chain to achieve sustainable development goals and reduce adverse impacts on the environment and society. Greenwashing is a misleading practice that severely threatens businesses’ sustainability. Greenwashing refers to the practice in which businesses intentionally mislead their customers about their environmental responsibilities. The present study aims to analyse, prioritise, and mitigate ways to reduce the impact of greenwashing on SSCM. The applied integrated Fuzzy Pythagorean Delphi-AHP approach evaluates 40 strategies identified through literature and by 20 highly experienced professionals. Contingency planning in case of disruption within the supply chain, ways of reporting and investigating charges for greenwashing, promoting environmentally friendly goods, imposing penalties in non-compliance cases, and completing circularity lifecycle assessments are identified as important strategies. The findings of the study will help supply chain and logistics managers build their SSCM for ethical, accountable, and transparent practices.