I read the Quanta article on this when it came out. They show the knots, and they're simple enough that I was almost surprised that the counterexample hadn't been found before. But seeing the shockingly complicated unknotting procedure here makes it much clearer why it wasn't!

It's interesting that you have to first weave the knot around itself, which adds many more crossings. Only then do you get a the special unknotting that falsifies the conjecture.