How to clean red tea stains from cracked glaze Japanese tea cups
For these types of cups with a cracked finish is the purpose is actually that over time, the tea fills up the cracks. This sounds a bit strange, but the same happens with porous Yixing clay teapots. The pores are filled with tea over time, which helps to improve the brew.

Given that you want to remove the strains I wouldn't use any detergent or soap. If that is sucked in the cracks it can be released when you serve tea in the future. This might negatively affect the flavor of tea.

To clean, I suggest the same method that's used to 'season' Yixing clay pots. You can cook the cup in hot water until the strains are gone.