Next time you need to get rid of snakes, either sell/give them to someone you know will take care of them or just release them yourself in the area you believe the mother to be from. I mean, all a wildlife official would do is put them somewhere away from people; there's not a lot of science to it, especially with a species as common as a garter snake. Though the best option is not to breed snakes if you can't care for or sell the babies.