In a manner characterized by grasping; with eagerness to grab or obtain, especially in a greedy or desperate way.
From grasping (present participle of grasp) + -ly adverbial suffix; describes an action done with the quality of grasping.
Adding '-ly' to an adjective is how English turns qualities into actions—'quick' becomes 'quickly'—and 'graspingly' captures that moment when desire becomes action, like a desperate grab for something precious.
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