"Hypertension markedly increases the risk of cardiovascular diseases and overall mortality. Lifestyle modifications, such as increased levels of physical activity, are recommended as the first line of anti-hypertensive treatment. A recent systematic review showed that isometric handgrip (IHG) training was superior to traditional endurance and strength training in lowering resting systolic blood pressure (SBP)"
I can't think of a mechanism for that effect, where something else wouldn't be probably better way to spend that effort. Like cardio training.