In the context of the high energy demand of large language models (LLMs) and growing concerns about global warming, there is significant demand for actionable recommendations that can help reduce emissions when utilizing such technologies. This paper examines the environmental impact linked to a fundamental function of LLM-based conversational systems that might be less well known to end users: the conversational memory, which enables the system to maintain context throughout the dialog. After analyzing conversation patterns using anonymized token data from a real-world system, a recommendation for individuals on how they could use chatbots in a more sustainable way is derived. Based on a simulation, the savings potential resulting from the adoption of such an ecological gesture is estimated.