As chatbots become increasingly integrated into group conversations on instant messaging platforms, concerns arise about their impact on user privacy. While prior research has examined chatbot risks in one-on-one interactions, little is known about how users perceive and respond to privacy threats in group settings, where chatbots may silently access messages and metadata. To address this gap, we conducted an online survey (N=374) across five popular messaging platforms—WhatsApp, Discord, Telegram, Viber, and LINE—to evaluate user awareness, understanding of chatbot access, privacy concerns, and behavioral responses. We found that many users were unaware of bots in their group chats and significantly underestimated their data access: only 41.7% correctly identified what messages chatbots could access. Privacy concerns also rose sharply after users learned about actual bot permissions. Based on our findings, we propose a five-stage model that captures how users detect, interpret, and respond to chatbot-related privacy risks. We further analyzed the designs of platforms with official chatbot support through this model and found mismatches between design choices and user expectations. Finally, we offer design recommendations to improve transparency and user control in group chatbot-interactions.