Multi-core fiber (MCF) imaging is essential for minimally invasive endoscopy in medicine and industrial inspection. However, the bulky distal optics increase the diameter and invasiveness, causing tissue damage. Its applications are further constrained by low spatial resolution and prominent honeycomb artifacts. We present a lensless MCF imaging approach based on Spectral-Guided Artifact Removal Network (SGARNet). In this framework, a physics-informed prior is embedded in a lightweight SpectralGate module to suppress lattice-frequency artifacts in the feature domain. The experimental results show a 12.12 dB improvement in PSNR and 0.4064 increase in SSIM, indicating superior performance over previous methods. The robustness and generalizability are confirmed by successful reconstructions across diverse textural complexities and biological tissue samples. These results demonstrate potential for practical deployment in compact and safer biomedical endoscopes.