From the looks of it this is Riverbank grape (Vitis riparia). And "your" problem is Black rot of grapes.
Honestly it's extremely hard to control it without full access to the plant: the first measure is sanitation, meaning throughly cleaning the ground from fallen leaves and especially eliminating all "mummies", meaning the affected grapes. The latter are a major sources of fungal spores and must be eliminated to reduce the amount of spores that will be released next year. This residue must be destroyed.
There are fungicides that will help keep manage Black rot but, again, since you have no full access to the plant I don't feel like suggesting wasting money to buy anything.
