Illā introduces an exception. After the general mention of her clothes, thiyābahā, libsata al-mutafaḍḍil singles out a light garment that remained.
Libsah denotes a garment or manner of dress. In this context al-mutafaḍḍil is a conventional description of light or informal dress. It must not be confused with the ordinary moral meaning of someone who grants favors.
The exception distinguishes between clothes laid aside for rest and a particular remaining garment. Interpreting the exception in relation to the preceding noun is more accurate than reading the words in isolation.