Applying open credit

Can some one please answer the question below

From time to time our builders send us checks for work that we have not yet completed or even started. When this happens they have to post the check (Or payment to that billing point) as on open credit. Subsequently we complete the work or partially complete the work and can bill it (Or again partially bill it). A/R person tells me that this is a very difficult process and that once she applies a portion of the check she looses visibility of the original document numbers.

I would want to think that applying a credit should not be that cumbersome and would like for you to explain to me the process Thanks