You can try calling back and checking with another customer service rep sometime. FWIW, I've been told the new parts system was designed to maximize tracking M&P's, AR's & revolvers, and the 3rd gen info is harder to access.
BTW, it's not like you're asking for a factory grip for a longtime obsolete gun, as the same grips are used on the 4013TSW.
Those are still in use by agencies. The ones we just replaced (with new plastic guns) were new production from the middle 2000's, and the CHP was still using some limited numbers of 4013TSW's until recently (might still have some not yet replaced, but I didn't hear the details).
They may not be making orders of replacement grips for commercial parts sales, but they probably still make limited orders for repair use. I don't know for certain whether the grips are made by the same plastic manufacturer that S&W has used for many years (and recently bought the company, in the last year or so), as they use any number of vendors.