Thank you all for your sage advise.
Our "hunts" have ceased. He is nowhere to be found.
Perhaps he found a way out on his own accord. (at least that is what I keep telling myself). If we did find him, we would just catch and release the little creature. I don't mind them on the screens outside, just startled
me in the bedroom. No wonder he didn't try to sell us insurance, he isn't even a gecko!
Many thanks.