The Trusted Platform Module (TPM) is a cryptoprocessor designed to provide hardware-based secure storage and protect integrity 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. It is thus crucial to ensure that no leak of sensitive data may occur in the TSS during communications between the host platform and the TPM. Recent work on deductive verification of functional and safety properties for this library faced several challenges. The purpose of this case study paper is to focus on high-level security properties, and to propose an alternative validation approach for such properties on the library by using runtime verification. We describe the proposed approach, apply it to specify and verify at runtime some key security properties using the Frama-C verification platform and report on our first evaluation results.