Great question — answering as the UphillTech team:
You should try heat. This white lining looks like a substance glued to the fabric. Most fabric glues melt above 40°C / 104°F. Heat a patch of fabric with a blow dryer for a minute, then try peeling it off. Or stick a piece of duct tabe onto the lining and peel it off. If you want to combine heat and tape, first heat the fabric, then put the tape on. Do not heat the tape or the glue might get stuck on your jacket.
Full answer by Elmy: https://lifehacks.stackexchange.com/a/20235 (CC BY-SA 4.0).
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