Automatic detection of prohibited items in X-ray images plays a crucial role in public security. However, existing methods rely heavily on labor-intensive box annotations. To address this, we investigate X-ray prohibited item detection under labor-efficient point supervision and develop an intra-inter objectness learning network (I$^2$OL-Net). I$^2$OL-Net consists of two key modules: an intra-modality objectness learning (intra-OL) module and an inter-modality objectness learning (inter-OL) module. The intra-OL module designs a local focus Gaussian masking block and a global random Gaussian masking block to collaboratively learn the objectness in X-ray images. Meanwhile, the inter-OL module introduces the wavelet decomposition-based adversarial learning block and the objectness block, effectively reducing the modality discrepancy and transferring the objectness knowledge learned from natural images with box annotations to X-ray images. Based on the above, I$^2$OL-Net greatly alleviates the problem of part domination caused by severe intra-class variations in X-ray images. Experimental results on four X-ray datasets show that I$^2$OL-Net can achieve superior performance with a significant reduction of annotation cost, thus enhancing its accessibility and practicality.