Similar situation nere me. Sun City Hilton Head ( actually in bluffton, 12 miles from Hilton Head!) has frequent incursions by "feral pigs". they contract someone to come in and 'remove them'.
It makes the news just about two times a year as homeowners whine, and then the animal rights ninnies complain how cruel it is to kill them. "They were here first!".
That argument is fallacious. The wild pigs were introduced by hunt clubs, and are NOT native to the area. The only reason they are around this area is to be hunted.