I have a bathmat like that. It's not skunk, it's the smell of the mat itself because it's new. The only thing that cures it is time. The smell will eventually go away. Until then, you might want to air it out daily on a clothesline or whatever, and that will help speed up the process.
I had the same problem with a cutting mat I bought years ago. I had to keep it in the plastic bag it came in for months, because it just smelled so bad. Now, it doesn't smell at all. So don't worry, there is hope!