This can be done in FileMaker Pro 9.
1. Add a number field to your table, let's call it "flagDone".
2. Change the priviledges so that the data entry folks can see/edit the record if the flagDone field is empty.
3. Create a script that populates the flagDone field with a 1.
4. Add a button to the data entry layout which performs the step 3 script.
And that's it!
The steps are simplified. For example, the script could also automatically omit the record, thereby avoiding the graying out that happens when one does not have the priviledges to view something.
You could use accounts and privileges to control that, however another option may be to have a bunch of global fields that they enter the data into and then script the writing process to the actual table since they have no access anyway. (Think web form)
I know you are asking for specifics but there are a lot of steps here and I am choosing to start with the big picture. From here, we can "drill down" to the level of detail you need to make this happen.
You should be able to do this using Accounts and Privilege settings. Reading up on this in the help system will probably be a good idea for familirizing yourself with this part of the system.
You can assign each contract manager an account and password. With this account, you assign a privilege set that specifies what layouts they can see and what records they can see and/or edit. You can then create a script that checks the privilege set name of the person who has opened the file. If it is the privilege set that you've assigned to your contract managers, the script can take them to their data entry layout where they can be restricted to just their records.
You'll probably want to use a value in a specific field that the contract manager uses to indicate that they have finished entering the data and which also "locks" the record so that they can no longer edit the database.
You can also learn more about this technique if you click the advanced search link and look for threads about "locking records" as there are a number of threads that have been created on that subject.
I think reading up on Accounts and Priviledges is great advice -- I needed to be pointed in a direction, and this might just be it -- I like to understand what I am doing!
The quick solutions are great too, however, and I am going to play with them a bit to see if I can make sense of how/why they work...
You can be sure I'll be back with more questions! :)