Interior Upgrade Question

[rebelz]

I've pulled out my old carpeting, to install a Heat/Sound Deadening material and new carpeting in my Z. I've come across a fastener, I'm unfamiliar with.
I need to remove the part in the first picture so I can remove the insulation to install the stuff & junk. It's held on along with the foam with the little round black fastener. Can this connector be removed without destroying it? If so how, if not what is it called and are new ones available?
Rich