If that box is plastic of any sort the Potable Aqua iodine will penetrate it and destroy either the box or the kit's contents over time. In any case the tablets will be ineffective and your kit may be damaged. Glass containers with teflon lids are required to properly store Potable Aqua.

I do not carry the tablets in my kit at all. Too many problems and too few tablets to be of much use. I carry a full bottle of PA in my vest pocket and consider this to be nearly inadequate (25L of purified water ain't much).