That's just a regular aftermarket dash cap. Someone may have glued it down, a lot of people just use velcro or on better caps I've seen them snug enough to hold themselves in place. I doubt your going to hurt anything taking it back up, since the reason most are put on in the first place is due to the original dash being cracked up.

Here is one vendor that sells these covers. Often you can find them on ebay or well, just about anywhere. I have a new unused on hanging in my garage.

http://coverlaymfg.com/lookup.html?parentURL=http%3A//coverlaymfg.com/&Reload=1449199347142