According to the San Diego Padres section of MLB Game Worn Jerseys of the Double-Knit Era, in the jersey section the Padres discontinued the pinstripe jerseys after the 2000 season, with the jersey style itself spanning from 1991-2000. However, when you look at the front section it lists the Padres as having a Home White Pinstripe in 2001.

The tagging style, according to KingJammy24's tagging era dates to the 2000 season, so it seems the tagging is appropriate.

With all that being said, I was not able to locate any images throuh Getty or elsewhere of any active players on the team wearing this style jersey in either 2000 or 2001. However, there are a few baseball cards, such as 2001 Bowman cards of Jake Peavy that show him wearing this style. (However, he was not on the big league club until 2002 and I'm not sure when the photo was taken.)

Another two possibilities for the jersey, if the style was not worn during the regular season, could be that the style was worn during 2001 Spring Training, but discontinued before the regular season and that's why the jersey would have been issued to Henderson, but we're not able to find photos. Or it could be a jersey that was used by Henderson to be introduced as a member of the Padres again, but I could not find photos of such a press conference. These are just thoughts and at this time I have nothing to back either idea.