Annotating remote sensing images (RSIs) presents a notable challenge due to its labor-intensive nature. Semi-supervised object detection (SSOD) methods tackle this issue by generating pseudo-labels for the unlabeled data, assuming that all classes found in the unlabeled dataset are also represented in the labeled data. However, real-world situations introduce the possibility of out-of-distribution (OOD) samples being mixed with in-distribution (ID) samples within the unlabeled dataset. In this paper, we delve into techniques for conducting SSOD directly on uncurated unlabeled data, which is termed Open-Set Semi-Supervised Object Detection (OSSOD). Our approach commences by employing labeled in-distribution data to dynamically construct a class-wise feature bank (CFB) that captures features specific to each class. Subsequently, we compare the features of predicted object bounding boxes with the corresponding entries in the CFB to calculate OOD scores. We design an adaptive threshold based on the statistical properties of the CFB, allowing us to filter out OOD samples effectively. The effectiveness of our proposed method is substantiated through extensive experiments on two widely used remote sensing object detection datasets: DIOR and DOTA. These experiments showcase the superior performance and efficacy of our approach for OSSOD on RSIs.