We have a fixed-price contract with a major government organization. I created the internal budget for this project and it equates to our staff spending 500 hours on the engagement. Three months go by and I see we utilized 450 hours. Then I came to know that one of the employees did not enter their time appropriately and we’re missing 100 hours. We are now 50 hours over budget and the work isn’t complete yet.
It's not clear what your question is. If this is a T&M contract where you are paid per invoice rather than a fixed sum, there may be some avenues within your contract to pursue the extra hours and re-budget the project. A construction attorney, especially one familiar with government contracting, can help you with this. But they will need a lot more information.