Mildew is one of those good news, bad news affairs. On one hand, mildew's presence means there's still some life in your leather. On the other hand, it's a sign that destructive molds are at work among the leather fibers.
Unchecked mold can also eat away at stitching, weakening the strength of any sewn tack parts.
Unfortunately, once mold spores get a toehold in your leather, completely removing them is almost impossible without damaging the leather itself. Under a microscope, the twisted tangle of leather's fibers resembles a network of fine plant roots. Anything strong enough to completely penetrate this tangle and kill every mold spore could harm the fibers or the bonds between them as well. The leather's structure and strength would be compromised. Protecting your leather tack from all contact with airborne mold spores is an impossible goal.