I would question this information. In the first place, the newer quickclot gauze products do not introduce "foreign material" into a wound as was a problem with the old free flow granules. The clotting factors remain in the gauze and the blood being clotted. I'd have to laugh at this argument anyway, since introducing loose particles of cayenne pepper would certainly be introducing "foreign material" to a wound, with no restraint on where it went afterwards.
To Use Cayenne Pepper Gauze
Remove debris and flush wound thoroughly.
Place cayenne-coated gauze on wound and add additional gauze pads to apply pressure.
Apply direct pressure for up to 10 minutes.
Remove gauze pad and wrap with clean bandage.
If bleeding does not stop, the wound may need stitches.
The suggestion to remove the gauze pad is completely counter to most emergency medical advice. Once a clot has formed, it is important not to disturb it unless/until the patient is in the hands of competent medical care/hospital.
All of my first aid and ER training calls for reinforcement of the dressing mentioned above, protecting it from further injury as much as possible. Ripping off the gauze with the clot would be seriously counterproductive.
As to cayenne pepper being analgesic, I have to laugh. It is a powerful irritant, and just touching it with intact skin burns many people. Applying it freely to raw tissue doesn't appeal to me. I have read that it will facilitate clotting, but have seen no clinical proof of it. If that was all you had on hand, might be worth a try, but I would seriously not expect it to be painless.