'granulocyte-associated' is a compound of 'granulocyte' and 'associated'. 'granulocyte' originates from New Latin (or Neo‑Latin) 'granulocytus', ultimately from Latin 'granulum' meaning 'small grain' and Greek 'kytos' meaning 'cell'. 'associated' originates from Latin 'associare' (past participle 'associatus'), where the root 'ad-'/''a(s)-' meant 'to/toward' and 'sociāre' meant 'to join or ally'.

'granulocyte' was coined in modern scientific/medical usage (New Latin/Neo‑Latin) in the 19th–20th century to name 'cells with small granules'; 'associated' passed into English via Latin 'associare' → Old French/late Latin forms → Middle English/early modern English 'associate'. The compound 'granulocyte-associated' is a recent technical formation used in biomedical contexts.

Initially, the elements meant 'small grain' (granulum) + 'cell' (kytos) for 'granulocyte' and 'to join/ally' for 'associate'. Over time these became a scientific cell-name and a general word meaning 'linked to'; the compound now means 'linked to granulocytes' in clinical and research contexts.