Hello again Just after posting I got two ideas:
1) Maybe I should use two times lower offset value, then the gap that I need? I mean, for example if I need a minimum gap equal 8e-4 m, maybe I shoud use offset 4e-4 m? This presumption I made, because maybe Mechanical adds two offsets, first for the Contact and second for the Target? And therefore I should use two times lower value than demanded gap?
2) I just read in Mechanical users guide:
"Offset: appears if Interface Treatment is set to Add Offset, Ramped or Add Offset, No Ramping.This property defines the contact offset value. A positive value moves the contact closer together (increase penetration/reduce gap) and a negative value moves the contact further apart."
So maybe I should use a negative value?
I added pictures of refreshed contact settings

Edit: @peteroznewman thank you for the answer, I posted before I read your message. Could you please verify and answer questions in my second post?