4040pd grips
The p/n 203560000 is the correct Smith & Wesson part number.
The mainspring fits into the hole in that black lug at the back/bottom of the grip.
If it then does not fit the 4040PD under the dovetail location, is possible that S&W sent you what they thought was the properly packaged grip.
It has happened in the past that the packaging of the grip was proper but the grip was not the correct one in it.
If you get the correct grip, it will fit perfectly, guaranteed.
On a side note for mags that will fit into a 4040PD and cycle perfectly and also lock the slide back:
The 39, 39-2, 3906 and 952, both 8 & 9 rounder's, the 8 rounder's from 3913LS and NL with both flat bottom and pinkie finger bases.
Doing a check with "dial caliper", they are dimensionally the same only made of Stainless Steel.
Regards,
BM1