Clean up as much of this as possible as the end of the summer season. If you are also interested in an experimental way to manage the disease, WSU fruit researchers at Mount Vernon have had good results covering the leafless trees in winter to keep the branches and trunks dry. They used clear plastic. One grower rolls his dwarf peach into the garage in December and January, thus keeping rain away from the plant. This method may be impractical if the tree's large, but it's worth trying on dwarf plants.
Infection occurs through the bud scales that cover next year's leaves.
The infection can get into the leaf bud just as it begins to swell, which may be as early as mid-December in a mild winter. As this is being written, the first week in December, temperatures have been relatively mild. Apply a fungicide once in mid-December, just as buds enlarge. Then reapply it twice more, timing 3 weeks apart. A sudden cold spell will make these dates later but the intervals remain the same.