How does one remove the plastic fasteners that hold the wheel well shroud?
Two situations: either to re-use, or to destroy and replace with a fender washer and a lag bolt.
Special tool exists?
Please see attached photo, thanks!

Front wheel well fastener, '15 Fit,

 

I don't think these fasteners are anything special.
Pull out the center portion a bit, and then the whole thing should come out.
Personal experience with made in Mexico fasteners is that they are brittle and break easily.
I had way better experience with made in Japan fasteners when I had Subaru's.
I bought an assortment of made in China fasteners from Amazon to replace anything that breaks.

 

Just use a flathead screwdriver and pry. I took that flap off 3 times in the last month doing VTC spring replacement and intake valve cleaning.

 

^^As stated above. Use a very small flat bladed screwdriver to pull the center disc section out......just 1/8" or so.
This action pulls a central stem and allows the 'clip' to compress, in order assume the diameter of the hole it lives in....so it can be inserted and withdrawn.

Yes, replacements are available on Amazon, but you have to be confident on what size to order.
These things come in many sizes.

I'm VERY FORTUNATE in that there's a body shop supply store near me which has all it's fasteners arranged on the wall on a sheet of plywood.
They charge 10 cents to 75 cents, depending on the clip.
You'll pay 10 to 20 times more per clip at a dealership.....IF they even have them.

 

You can buy bunches of these fasteners on Amazon, either a single size or a mix of different sizes. Fairly cheap. The dealer will hose you for a single one.. Size of the fastener is determined by the size of the hole that they fit into. A 10 mm diameter hole requires a "10 mm" fastener. I would recommend replacing them with a new fastener every time they are taken out. Although they can be used several times their holding ability deteriorates every time you re-use it.