The Trusted Platform Module (TPM) is a cryptoprocessor designed to protect integrity and security of modern computers. Communications with the TPM go through the TPM Software Stack (TSS), a popular implementation of which is the open-source library tpm2-tss. Vulnerabilities in its code could allow attackers to recover sensitive information and take control of the system. This paper describes a case study on formal verification of tpm2-tss using the Frama-C verification platform. Heavily based on linked lists and complex data structures, the library code appears to be highly challenging for the verification tool. We present several issues and limitations we faced, illustrate them with examples and present solutions that allowed us to verify functional properties and the absence of runtime errors for a representative subset of functions. We describe verification results and desired tool improvements necessary to achieve a full formal verification of the target code.