Negotiate giving it back.
Guarantee full independence, own tax law, control of territory, etc.
Make it last at least a generation.
If you look at the existing small population (less than 4k), people would have time to make plans.
Anyone born there can get a Brit passport and go elsewhere or stay.
The place has got to be a money pit for Britain. Oil and mineral profits can be negotiated. Milei speaks strongly for a negotiation while Yahoo interprets it as threatening-fake news.
The US. Turn the place into a penal colony for border crossers. No transportation in or out. Work with them. Win-win. Brits? No big deal as they invented racism.