I turned an old T-shirt into a rag and used it for cleaning.
Those clothes are already like rags.
雑巾 is a floorcloth or dustcloth, typically made from old cloth but used specifically for wiping floors or surfaces. ぼろ布 is a more general term for any old rag or scrap cloth, not necessarily for cleaning.
布切れ is a neutral term for a piece of cloth, not necessarily old or worn. ぼろ布 emphasizes that the cloth is tattered or of poor quality.
Common mixed kanji-kana spelling. The reading ぼろぬの is also possible but less common.
Katakana variant of ぼろ, often used for emphasis or in informal writing.
Katakana variant of ぼろ切れ.
Alternate spelling using 切れ for 'piece of cloth'.
Rarely used kanji form; 襤褸 is a complex ateji for ぼろ.
Compound of ぼろ (onomatopoeic/mimetic word for something tattered or worn) and 布 (cloth) or 切れ (piece). The exact origin of ぼろ is uncertain, but it is likely sound-symbolic.