No way to adjust it. I think it sets atop molded plastic that extends down from the dash so removing it would be ugly at best.
I sat in a ST2 today in Glendale, Ca ( Glendale is a small city just north of LA - the closest dealer to Dodger Stadium where the Performance Academy will be held this Saturday ) while they were in line for maintenance in preparation for the Academy.
There is no way to adjust it, but the plastic is not one contiguous piece. One long piece comes all the way down from the dashboard, but the part directly under the arm rest is a separate piece. It is sort of rectangular box, about the size of a shoebox, sitting on its end. It fits inside a approx 5" x 6" hole in the main part, as if it had been dropped in. It looks like it could be lifted out, chopped a bit, and put back in, resulting in a lower arm rest.
There are some complications in doing so. There is a back seat cigaret lighter in the rear of it which must have wiring, and there are USB port connectors inside of it under the rest. Disturbing these might be tricky.
Unless some Hyundai dealer makes me a heck of a deal on a Veloster Turbo, I'll be buying an ST... and doing some surgery on it. I'll post result here with photos.