The use of the past tense in this construction, especially when spoken, is often used to express emphasis and, perhaps frustration.
We already GAVE him a response.
We just GAVE him a response.
These forms are used to indicate that the recipient is somehow not being reasonable in continuing to seek further feedback. The sentences would have less "punch" if they were delivered as
We HAVE ALREADY GIVEN him a response.
We HAVE JUST GIVEN him a response.