Olfa recommends soaking your mats and as long as you lay them flat to dry out, it's ok to curl a little in the tub while soaking. The material in the mat which makes it self-healing doesn't work well when it's dried out which is the reason for the occasional soaking.
If you are getting rid of your mat - remember that it can be cut up...use part as a template for folding fabric for your shelves, use another long piece for the end of your ironing board to use as a cutting mat when making the continuous bias binding, some could be covered to make a stiff, yet flexible cover for a journal....etc...and I like the shoe mat idea.