Hold the phone.
The mechanism you circled is for opening the door, not the lock.
Did you mean you can’t open the door from the outside?
If that is the case there are two places that can be worked with.
The door button has a pin on it that presses a paddle looking part on the mechanism.
If that piece that the pin presses is bent the pin may not be able to press it far enough.
Alternatively, you might be able to bend that paddle looking piece closer to the pin.
It’s also possible that the door button isn’t traveling as far as it is supposed to because of lack of lubrication or the little paddle it presses against is corroded causing the button pin to hang up as it slides across the surface.
From my experience it’s usually one of these two issues.
First check the surface on that paddle and see if it’s all corroded.
You can do this by pulling the paddle away from the pin and feel the surface the pin pushes against.
If it’s grooved or rusty you might want to remove the mechanism and clean/repair that surface.
Wheel bearing grease works well for where the pin hits.
I could see slightly taking a little of the bend out of the rod and see if that helps if needed, but I would start by lubing all those moving parts.
That itself could solve the problem since they look so dry.