're-dye' is formed from the prefix 're-' (originating from Latin 're-', meaning 'again') attached to the verb 'dye' (from Middle English 'deyen', from Old English roots meaning 'to color').

'dye' was used in Middle English as 'deyen' and developed into the modern English 'dye'; the productive prefix 're-' was attached in Modern English to create 're-dye' meaning 'to dye again'.

The element 'dye' originally meant 'to color (cloth or material)'; by forming 're-dye' the meaning became specifically 'to color again' or 'to restore/change color a second time'.