Web agents, like OpenAI's Operator and Google's Project Mariner, are powerful agentic systems pushing the boundaries of Large Language Models (LLM). They can autonomously interact with the internet at the user's behest, such as navigating websites, filling search masks, and comparing price lists. Though web agent research is thriving, induced sustainability issues remain largely unexplored. To highlight the urgency of this issue, we provide an initial exploration of the energy and CO₂ cost associated with web agents from both a theoretical —via estimation— and an empirical perspective —by benchmarking. Our results show how different philosophies in web agent creation can severely impact the associated expended energy, and that more energy consumed does not necessarily equate to better results. We highlight a lack of transparency regarding disclosing model parameters and processes used for some web agents as a limiting factor when estimating energy consumption. Our work contributes towards a change in thinking of how we evaluate web agents, advocating for dedicated metrics measuring energy consumption in benchmarks.