Field dodder (Cuscuta campestris) is a parasitic, annual plant that extracts water and nutrients from the vascular tissues of its host. Field dodder lacks chlorophyll so it cannot photosynthesize its own food. In your case, it is the hydrangea plant’s vascular tissue that is feeding both the field dodder and the hydrangea. Field dodder produces a dense mat of yellowish, leafless, threadlike branching vine that branches and roots in your plant.
You can't use a herbicide on field dodder because it takes its nutrients from your hydrangea plant. You will have to take out the hydrangea plant to kill the field dodder. The weed came in as a very small seed. It is important not to let this plant flower; otherwise, more plants will be infected next year.