'slender-billed' originates from Modern English as a compound of 'slender' and 'billed', where 'slender' meant 'thin' and 'billed' is the past-participle/adjectival use of 'bill' meaning 'beak'.

'slender' came into English via Middle English 'slender' (with senses of 'thin, slight'), possibly influenced by Old Norse; 'bill' (sense 'beak') comes from Middle English 'bille' (compare Middle Dutch/Middle Low German) and developed to mean the beak of a bird, so the compound combined those elements in modern English.

Initially, the components meant 'thin' ('slender') and 'beak' ('bill'); over time the compound evolved to specifically describe birds with a thin or narrow beak ('having a thin beak').