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Large language models (LLMs) have recently transformed many industries, enhancing content generation, customer service agents, data analysis, and even software generation. These applications are often hosted on remote servers to protect the neural-network model IP; however, this raises concerns about the privacy of input queries. Fully Homomorphic Encryption (FHE), an encryption technique that allows computations on private data, has been proposed as a solution to this challenge. Nevertheless, due to the increased size of LLMs and the computational overheads of FHE, today's practical FHE LLMs are implemented using a split model approach. Here, a user sends their FHE encrypted data to the server to run an encrypted attention head layer; then the server returns the result of the layer for the user to run the rest of the model locally. By employing this method, the server maintains part of their model IP, while the user still gets to perform private LLM inference. In this work, we evaluate the neural-network model IP protections of single-layer split model LLMs, and demonstrate a novel attack vector that makes it easy for a user to extract the neural network model IP from the server, bypassing the claimed protections for encrypted computation. In our analysis, we demonstrate the feasibility of this attack, and discuss potential mitigations.