This is a "leaf spot" infection, a catch-all term for a variety of pathogens causing this type of disease on many different species of plants. The pathogens responsible can be fungi or bacteria, and symptoms often look alike; hydrangea can contract both, though the pictured symptoms do look fungal.

In either case, despite being an eyesore, they are not serious with regards to long-term plant health impacts. No fungicide use is recommended, nor would it be able to cure existing disease. The gardener can remove heavily-spotted individual leaves if they want for aesthetics, but it's not necessary.

Maintaining good air circulation around vulnerable plants (avoid overcrowding with dense planting, or pruning out some stems every year or so if they become too crowded) can help to reduce the spread and severity of leaf spot diseases, though weather also plays a role. If the hydrangea is irrigated in such a way that wets the leaves (or, say, a nearby lawn sprinkler wets the shrub), avoid this and only water the soil, as wet foliage can be easier for spores to infect. (Or, make sure watering is done early in the day so the foliage can dry by nightfall.) Raking-up and disposing of fallen leaves this autumn/winter from infected plants might help to reduce the likelihood of a repeat infection next year, though it could still occur from spores blown-in to the area.

Miri

You're welcome.