What does the cryptic crossword clue "Closely-woven material taken to the cleaners (7)" mean?

The definition is "Closely-woven material / taken to the cleaners". The wordplay uses a double definition. Double definition The answer is WORSTED.

Closely-woven material taken to the cleaners (7)

Times Cryptic #29003 | 8 Down | 2024-08-23 flower