Detecting multimodal misinformation, especially in the form of image-text pairs, is crucial. Obtaining large-scale, high-quality real-world fact-checking datasets for training detectors is costly, leading researchers to use synthetic datasets generated by AI technologies. However, the generalizability of detectors trained on synthetic data to real-world scenarios remains unclear due to the distribution gap. To address this, we propose learning from synthetic data for detecting real-world multimodal misinformation through two model-agnostic data selection methods that match synthetic and real-world data distributions. Experiments show that our method enhances the performance of a small MLLM (13B) on real-world fact-checking datasets, enabling it to even surpass GPT-4V.