I have ordered that part from Numrich in the past, and it does not actually work in my 3913 magazines, which need a flat buttplate catch assembly rather than this stepped one. My guess is that the one Numrich sells is really for the older model 39 magazines.
The S&W part # that you will need is 239720000, and can be ordered from S&W themselves over the phone (1-800-331-0852 ext. 4125). It has been a flat metal part in the past but I think now you will receive a plastic one, and you can see what it looks like on Midway's website:
Smith & Wesson Mag Floorplate Catch Assembly S&W 3953TSW CS40C CS40D
*Edited to add some pics of the 2 different 3913 BPC assemblies (plastic one & middle one), and the one that Numrich sold me (the metal one on top/right).