Not related to BP's question, except that I was looking at something and wondering the same thing. My thing is a screwed-on peg-like attachment on my topeak saddlebag. I have just, after many years, discovered that the metal piece unscrews. No idea why.
Total guess:
You put a pump through the loops on the bottom and clamp the pump head to the valve simulacra.
That's a nice deduction. I thought it looked like a pump peg, but it hadn't occurred to me that it was to hold a pump in that orientation. But I couldn't imagine how it would hold a pump in the frame either.
Descriptions of the Topeak Aero wedge say the medium and large versions have a built in pump holder, so I imagine that's it.
Sam
Aha! Thanks Sam. I did do a search generally and on the Topeak site specifically, but didn't find that.
It's a bit of a compromise - the peg seems only to suit a pump head adapted for schrader valves. But if that's your only way of carrying a pump I suppose the inconvenience might be worth it.