[lugerholsterrepair]

James..The strap you show on your pistol looks to be a home made aid to pistol extraction as indicated by David and he is correct. The Swiss were quite fond of this handy device. You see a short lanyard sewn permanently onto Swiss pistols fairly frequently whereas you don't on German pistols.
The photo posted by Rich is my answer to keeping stress off of the pull-up strap of your holster when you take out the pistol cause if you break it..it's bad.
Mine is also removeable so you can transfer it one to the other. I also use one at the range as a steadying brace as it lays on my wrist.