This term means the process of "re" hewing timbers as part of the layout/cutting process to make the timbers closer to square and closer to dimension. It is done when laying out by the square rule on hewn material. When you snap your layout lines (at say 2" from the edge), there will be places that due to irregularities in the hewing will stick out more than 2" from the layout line. Counter hewing is the process of hewing off the places that are "proud" of the theoretical edge.
This can be done just at the joints or on the whole stick. If it is done just at the joints then at the tenons, it is basically reducing both sides of a tenon.
I think this would have been an important part of the process when a carpenter was using timbers that were supplied (or hewn) by the farmer/owner, which in my understanding, was fairly common. (We all know what it is like to follow someone else's work.)
Now, you've got to tell us more about the contract! Where, when, what, how big, how much, did it include the raising or just framing/counterhewing?