Multimodal large language models (MLLMs) are increasingly adopted in remote sensing (RS) and have shown strong performance on tasks such as RS visual grounding (RSVG), RS visual question answering (RSVQA), and multimodal dialogue. However, hallucinations, which are responses inconsistent with the input RS images, severely hinder their deployment in high-stakes scenarios (e.g., emergency management and agricultural monitoring) and remain under-explored in RS. In this work, we present RSHallu, a systematic study with three deliverables: (1) we formalize RS hallucinations with an RS-oriented taxonomy and introduce image-level hallucination to capture RS-specific inconsistencies beyond object-centric errors (e.g., modality, resolution, and scene-level semantics); (2) we build a hallucination benchmark RSHalluEval (2,023 QA pairs) and enable dual-mode checking, supporting high-precision cloud auditing and low-cost reproducible local checking via a compact checker fine-tuned on RSHalluCheck dataset (15,396 QA pairs); and (3) we introduce a domain-tailored dataset RSHalluShield (30k QA pairs) for training-friendly mitigation and further propose training-free plug-and-play strategies, including decoding-time logit correction and RS-aware prompting. Across representative RS-MLLMs, our mitigation improves the hallucination-free rate by up to 21.63 percentage points under a unified protocol, while maintaining competitive performance on downstream RS tasks (RSVQA/RSVG). Code and datasets will be released.