The Nostalgic Fabric is a key item from Tears of the Kingdom.
Tears of the Kingdom
"Tough fabric bearing a nostalgic design. It looks like it could be used to make a paraglider"
The Nostalgic Fabric can be found in a chest in the tower of the Temple of Time Ruins on the Great Plateau, the same location where Link received the paraglider from King Rhoam's ghost in Breath of the Wild.
The "nostalgia" in question is that it matches the fabric from the Breath of the Wild paraglider. As such, when used by Sayge at the Kochi Dye Shop to rework the paraglider Purah gives Link at the Lookout Landing Skyview Tower, the newly-reworked item resembles the paraglider Rhoam gave Link.
Paraglider icon when reworked with Nostalgic Fabric