John, I felt like you when I wound up with them. But then, I started catching some. They're ugly mutts. I tossed them on the bank at every opportunity. However I found that a 5 inch GSF out fought a 7 inch BG or HBG. If they get to 8 inches, you need stronger line. I think my last one was about 9 to 10 inches and old the last time I caught it. After that, I pulled my hook away from hi/her/it just to keep from injuring it. It finally disappeared.
They spawn annually so mine disappeared after about 5 years. Then a creek overflowed into my forage pond and I got some more of them. I no longer worry about them and no longer look at them as a weed in the garden. I love the fight. If I had a pond to dedicate to them, I'd do it in a heartbeat.
However, if a pure HBG pond were my goal, I'd probably be upset. Other than killing the pond and starting over, I doubt that you can do anything about them.