Fatboy,
When I refer to a relaxed grip, I am referring to the basic grip people use between tight grips when ascending and descending stair flights on the handrail.
When out and about I tend to watch people using stairs and handrails, mainly since that is my area of focus besides guards and doorways.
Pay attention to how you use your own hands when moving up and down stair flights.
It is rare I see someone keep their hand grasped around when descending, normally just pressure down on top with the palm and then fingers slightly outward.
However, when ascending people with a need to pull themselves up do cup their hand under and slide, but have to move the fingers outward when passing a support bracket. Either way they always set before sliding past a support when using the handrail to ascend.
So when I talk about a relaxed grip, my point is, the hand at some time during the climb needs to release in order to move, vs. a tight grip.
It becomes second nature, just as the gait of your steps are for tread and riser.
Regards T