How do I remove the magazine catch on my 3913? I was trying these instructions that I found:
"Use a small jewelers screwdriver set, pushed the lill retaining plunger down and unscrewed the button. Be careful NOT to launch that retaining pin!!! Take the pin and spring out, the mag catch should fall thru."

While I was able to push in the retaining pin (that's the one in the center of the mag catch button, correct?), I was not able to unscrew the button. It just would not turn at all.

Is this the correct process? Or is there something else that needs to be done before I can get that button out?

The retaining pin is the small pin (((((((next)))))) to the mag catch. I'd use a small punch and not a screwdriver, but that's me.
Here's some helpful disassembly info also
Disassembly instructions for a 4006

Hmmm...
According to the webpage you mentioned:
"If you want to remove the mag catch, you will need to use a punch to depress the plunger that holds the mag catch captive on the left side of the frame. With the plunger depressed, you should be able to unscrew the mag catch button. After that, you can remove the plunger and its spring, along with the actual mag catch."

So now I'm confused; is the "thing" that I'm going to be depressing located in the middle of the mag release button on the left side of the frame, or is it the pin next to the mag release on the right side of the frame?

Here's a pic of a couple different Gen 3s, one's on top the other on the bottom.



Push the small pin next to the catch in, then turn the mag catch with a small screwdriver.

Hope that helps

Dave

Terrific!

Pictures help so much...I WAS pushing down on the wrong part.

Thanks!