I don’t think neanderthals knew how to chemically tan leather.

They had skins from hunting, knives for scraping, and awls for sewing.

The earliest examples of leather tanning come from the middle east in about 7000 BCE where they were using urine, feces and one step shy of basically leaving the skin to rot to do so. I can only imagine a hunter gatherer tribe of neanderthals’ who’s species was all but totally incorporated into homo sapiens or died out 21,000 years before that didn’t have a terribly great handle on leather tanning. My guess is their experience was hide garments were just raw hide that had been perhaps dried over a fire or by the sun and rubbed with a mixture of ash and urine to incidentally tan the hide