When you receive a check and record it in the Claim Ledger, you can note what amount and for what the check/money is to represent.
Demands and Offers tracks how much money you have calculated a loss is worth, and what the final settlement for that loss will be paid from the carrier. Payments don't come into play yet. Once a check is received, you record it in Claim Ledger (think of it as Accounts Receivable.) After checks are recorded, you 'disburse' them - including your company fee and the amount your client keeps. From your company fee, you can determine how you pay out that money - expenses per claim that need to be paid as well as how much you pay each of your assignable (adjuster, estimator, apprentice, etc.) users on that claim.