'unstarched' is formed from the negative prefix 'un-' (Old English) plus 'starched', which comes from 'starch'.

'starch' derives from Old English 'stearc' (stiff), from Proto-Germanic *starkaz; it became Middle English 'sterchen'/'starch' and later the verb 'starch' and adjective/past participle 'starched', with 'un-' added to form 'unstarched'.

Originally related to 'stiff' or 'to make stiff' (by applying starch); 'unstarched' has the straightforward opposite meaning of 'not stiffened by starch' or 'not treated with starch'.