In a manner characterized by grunting; with grunts or while making grunting sounds.
From grunt (verb) plus -ing (present participle) plus -ly (adverbial suffix), creating an adverb describing an action performed while grunting.
English lets us add suffixes almost endlessly—gruntingly shows how we can convert any verb into an action-describing adverb, which is why English can express almost any 'how' even without pre-made words.
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