"grasp the connection" is correct and usable in written English.
You can use it to describe the act of understanding a relationship between two ideas. For example, "If you want to understand the complex economic systems, you need to first grasp the connection between supply and demand."
That is understandable, but it makes it harder to grasp the connection between Mills's life and work.
He says this is something to do with the far right gaining ground, but it's hard to grasp the connection.
By going to the courts to stop it being shown, the Indian authorities reveal themselves to be unable – or unwilling – to grasp the connection between the two.
By contrast, dogs seem to instantly grasp the connection.
They hold that to be justified in a belief not only must we have evidence that supports the belief, but we must "grasp" the connection between the evidence and the proposition believed (Fumerton, 1995: 183–224) This grasping of evidential relations may strike some naturalists as exceedingly dubious.
Humanistic psychologist John Amodeo says Satin is one of the few political theorists to grasp the connection between personal growth and constructive political change.
If you pay attention, you see what is going on and grasp the connections between the different things you see, none of which are terribly unfamiliar.
The central concern of the theory of collective intentionality is to grasp the connections and interactions between the mental and the social.
The court ruled that a reasonable person would have grasped the connection between the symptoms and the abuse much sooner.
But its government seems, at last, to have grasped the connection between Japan's miserable showing in international entrepreneurial rankings (see chart) and its economic malaise (though a very high proportion of entrepreneurs can sometimes be a sign of structural problems for bigger companies, as in Thailand).
One needn't have grasped the connection between sexual intercourse and pregnancy in order to be the cause of a child's existence.
