I drew one of the coveted Bull depredation tags on the Wichita Mountains National Wildlife Refuge outside of Lawton, OK.
Tags issued for hunts within the refuge are not for "depredation" purposes. The USFWS has a target number of animals that they maintain for the refuge; excess numbers of deer and elk are culled via hunters who participate in a drawing, while bison and longhorns are rounded up and sold at auction.
Depredation hunts are for the animals that've escaped onto private land surrounding the refuge. This was all covered in your pre-hunt briefing you attended the day prior to the hunt actually commencing. I've hunted the refuge three times; twice for deer in 1995 and 2005, and once for elk last year.
FYI, the refuge is managed by the USFWS, not the National Park Service.