If you mean what Smith calls the "Trigger Play Spring", I replaced my 1006's sometime around 1990. I bought a bunch of spare parts at that time which included a couple of these springs and brads. I think I replaced mine thinking a new spring would "tighten up" the trigger. In fact, it made no difference.
I don't remember exactly what I did on a step by step basis, but I do seem to remember the little brad that holds it in place is rather soft Aluminum. I either just yanked the spring off and then squeezed down the brad's "petals" with needle nose pliers to remove it or did that in reverse order.
Installing the new spring and brad was about as simple. Once in place, the soft brad was easy to peen. Best I recall, I did that with a brass punch and small brass hammer. It "squashed" out flat pretty easily. The replacement spring and brad have been there through several thousand rounds since and it hasn't loosened a bit.