After being unable to twist the screw out, i resorted to doing it properly.
Start off by unscrewing 6 tiny screw and taking off the back panel.
Then take out the button sliding part (hold the tiny spring!!!)
and the top (hold the tiny spring!!!)
Now with access to the inside, we see the culprit. Pry it off.
Luckily, Garmin is sane (unlike RAM with their 11mm nut for a large-pitch threaded U bar...) and uses a standart pitch M3 thread. So to a bolt shop I go.
You know the standart screw has threads only at the very end and the thinner stalk moves freely in the hole in the top plastic part. I needed to duplicate that, except that I chose to leave a few more threads at the end.
And if you don't have a lathe:
The standart bolt stops not when the threads go all the way into the well, but when the bolthead touches against the plastic - so it's ok the leave more thread at the end as long as there's something on our new bolt to push against the plastic top part (to mimic the standart bolthead).
In my case, a long "handle":
Put the new bolt in with,remembering it's cone shaped spring, then slip on the retaining clip from the inside (you can leave it out if you think there will be a need to remove the lock screw without taking the mount apart again).
Then put the 2 plastic parts together. Do I need to mention the tiny springs?
They fly far once being bounced off your head and can only be found by lucky chance inside some camera cases.
And don't think breaking a lighter will save you!