See also Resolving Debts for a short discussion on debt forgiveness.
To pay some or all of the amount owed on a debt,
If you make a partial payment, the next time you click the "Paid" cell you will see a dialog listing all payments for that debt to date, as well as a button to add a new payment.
To keep the estate accounts balanced, EstateExec will also automatically record any debt payment as a transaction on the Cashflow tab: you don't have to do anything extra.
Alternately, you can choose to enter payments directly via the Cashflow tab (it just takes a few more clicks):
In addition to creating the transaction, EstateExec will automatically reduce the amount owed on the Debts tab. It doesn't matter whether you enter the payment via the Debts tab or the Cashflow tab; the results will be the same, and reflected everywhere throughout EstateExec.