Large Language Models based Table Question Answering (LLMs-based TableQA) models excel in NLP field, however, they occasionally exhibit an unfaithful behavior where correct answers are derived through erroneous reasoning paths. In this condition, we propose TrustTable, a neuro-symbolic framework designed to ensure reasoning faithfulness by auditing the reasoning processes of LLMs. Unlike monolithic LLM-based auditors, TrustTable decouples the auditing operation into two orthogonal dimensions. It enforces factual grounding by executing neurally generated Pandas code against the table, and ensures logical soundness by verifying reasoning chains through a LLM-synthesized formal solver. By integrating these symbolic checks, TrustTable enables a Label-Free Audit Loop that systematically identifies and rectifies reasoning flaws without human supervision. In addition, we present the TrustTable-Bench, a diagnostic dataset containing diverse error categories that range from calculation discrepancies to schema misalignments. This benchmark allows for a rigorous quantification of reasoning limitations. Experiments demonstrate that our symbolic audit detects reasoning flaws more accurately than advanced baselines. More broadly, the TrustTable outperforms LLM judges in both majority voting with logical weighting and rejection sampling with process supervision.