Unable to remove my bathroom recessed lock

Question

I want to repair my recessed lock, it broke some time ago and I have to replace it, but I have an issue. This is a bathroom lock and, I cannot remove it from the door, because the "bathroom spindle" is stuck in the mechanism with some metallic jaw.

Here are two photos to understand the setup:

And here is a zoom at the thing preventing me from removing the bathroom spindle:

Do you have any idea how to remove it, should I just hammer the spindle until it moves? It seems a bit rusty as well!

Answer 1

For those who might come on this topic later (if you ever search for this), this is in fact a model sold at the BHV (bazar de l'hôtel de ville) in Paris. You can find the exact same mechanism and the only solution to remove the part is to force because the metallic jaw can be gripped on the metallic bar. This is a bad mechanism...

I broke a porcelain ring by removing it. But you can buy spare parts at the BHV. See the complete kit for example.