If you choose "Cash" as one of your collection methods, those who owe you money have the ability to mark that they've paid you via cash within the same form where they would also be able to use a credit card or PayPal to pay you back.
If they did not actually pay you back, that is no problem and you can simply delete that cash payment.
To do so,
(1) Go to your Expense tab on Travefy and click "Payment History" in the top right corner.
(2) On your Payment History Page you will see a list of Transactions. Simply click on the edit (e.g., pencil) icon next to the cash payment in question.
(3) This now opens up a form field for this payment. Just click the "Delete" button in the lower left-hand corner and this cash payment will be deleted. All balances on your Expense page will also be reflected.