fade, discolour
褪 centers on loss of color or intensity: fading, discoloring, or losing vibrancy. The idea extends naturally to taking off clothes, as if color is being removed.
褪 combines 衤 (clothing) with 退 (retreat, withdraw), suggesting color withdrawing from cloth or clothes being removed. The phonetic role of 退 is uncertain.
Clothing 衤 that retreats 退: imagine a shirt fading in the sun as its color retreats, or someone taking off a garment.
For タイ, picture a tie fading in the wash: tie -> タイ, and the color retreats from the fabric.