I had this white line exactly as you described it and tried every chemical I could think of - nothing had any effect. I could remove it with a razor blade but it was so difficult that it was not a practical solution. I finally solved the problem using an Aussie product called Rok Blok which is like a pumice stone but is softer and artificially manufactured from crushed glass particles. This worked remarkably well and did not scratch the glaze. Unfortunately your tiles are not smooth and glazed like mine so I am not sure how well this would work for you. The downsides of this rubbing block were the expense (about $10.00 AUD each if bought in a pack of 10) and the fact that they wear away quite rapidly.