Single-view 3D reconstruction methods like Triplane Gaussian Splatting (TGS) have enabled high-quality 3D model generation from just a single image input within seconds. To prevent such infringement, we propose a novel image protection approach that embeds invisible geometry perturbations, termed geometry cloaks'', into images before supplying them to TGS. These carefully crafted perturbations encode a customized message that is revealed when TGS attempts 3D reconstructions of the cloaked image. Unlike conventional adversarial attacks that simply degrade output quality, our method forces TGS to fail the 3D reconstruction in a specific way - by generating an identifiable customized pattern that acts as a watermark. Extensive experiments have verified the effectiveness of our geometry cloak.