There is no telling when it was made! Some guns were shipped YEARS after they were made. Instead, S&W kept/keeps records by the shipping date from the factory. The Standard Catalog of Smith & Wesson has a fairly close record of that info.
The only way to know 100% for sure the ship date is too call S&W at their toll free number and tell them the serial number...or, for $30 one can obtain a factory letter specific to the gun. It's usually not worth doing that unless it is a rare gun, or perhaps has some interesting provenance regarding original owner, distributor, etc.
If you will give me the serial number (from the bottom of the grip frame) I'll be glad to look it up and give you a very probable ship date from S&W. Include all numbers including any prefix. Block out the last numbers if you wish with an X...one X for each number you don't indicate.
Some folks have a concern regarding the posting of serial numbers. The X's should aleviate any concerns. If not comfortable with that, feel free to PM me or shoot me an e-mail.
The thing on the grip is a Tyler T-grip. The company is still in existence and has a web-site. Just do a search for "Tyler T-Grip" and it will show up. The T-grips also appear on Ebay upon occassion. You would need one for a J-frame S&W round butt if your gun is like mine. The web-site will cross reference your gun to a Tyler item # for the right adapter.