I have a wall in the bathroom that had a mat on it and now I'm going to change the mat and wonder how you would do it, sand off the glue residues and fill or put on a panel to avoid a lot of sanding work but then you'll probably have a lot of drilling and plugging work instead!? Or can you glue a panel and just put some screws? Tips are welcome 
If the wall were straight, I would probably glue the board. Otherwise, I would have framed it with fairly thin studs to straighten the wall.