It looks like it is actually a piece of tubing that has been flared at each end.

You can pick up a flaring tool at Harbor Freight (or I can loan you mine) & you'll just have to find the right sized tube at your local hardware store (or plumbing or air conditioning supply store).

It shouldn't be too complicated & you can practice on a scrap piece before you get started so you can make sure it'll work out for you.

The flaring tool will just spread out the diameter of the tube so that it won't go back through the hole. If you want to actually curl the edge of the tube over (like shown in the picture), you can pick up a cheapo snap repair kit at Lowes that has a punch like thinggy that you hammer onto the end causing that curling effect (I have one of those too if you need to borrow it).