Use a heat gun to heat up the bedliner at the corners of the pickup bed. Once it’s hot enough, you might be able to peel back the liner.
Pour Xylene, acetone, or other chemicals onto the bedliner and allow it to sit and soften. Be extremely careful when using these chemicals—take care to be in a well ventilated area. Be sure to use a breathing mask.
You can also sandblast the pickup bed. Sandblasting can be extremely effective at removing metal finishes without damaging the underlying metal. Many local paint shops will handle media blasting your pickup bed.