GPS trajectories encode rich behavioral information about how people move, organize activities, and form daily routines. Recent advances in large language models (LLMs) raise a natural question: can such models infer and summarize travel behavior directly from mobility traces? This paper introduces TravelBehaviorQA, a large-scale benchmark dataset that reframes trajectory analysis as a language-based behavioral understanding task. The dataset links raw GPS trajectories with human-grounded question-answering (QA) pairs that capture travel intensity, temporal structure, activity patterns, mode usage, and behavioral routines. Unlike prior mobility datasets focused on prediction or classification, TravelBehaviorQA emphasizes semantic interpretation through a unified mix of deterministic and open-ended questions. In this benchmark, we construct over 143k QA instances spanning users and years, and evaluate a broad range of state-of-the-art LLMs under controlled settings. Our results reveal substantial gaps between factual extraction and genuine behavioral reasoning, showing that model scale alone is insufficient and that trajectory representation is a primary bottleneck. TravelBehaviorQA exposes critical limitations of current models and establishes a rigorous benchmark for advancing language-based understanding of human mobility behavior.