How would I apply a check for a settlement that I do not have an invoice or account for... ?

Hello, @milly6180.

You can use the Sales Receipt or Record Deposits to record it in your QuickBooks Desktop for Mac. Just make sure that when creating a Sales receipt, you’ll select the check as a payment method.

Here’s how.

1. On the QuickBooks home screen, select Create Sales Receipts.
2. From the Customer: Job drop-down, select the customer.
3. Fill in the relevant information.
4. Choose the payment method as Check.
5. In the detail area, fill in the description and amount received. 
6. Then, click Save & Close.

Also, you can directly record your check to Record Deposits and contact your accountant so you’ll be guided for the correct account. 

You can also check out this article if you wanted to customize a customer job or sales receipt in QuickBooks. Customize reports.

Let me know if you have any other questions. I am here to help. Take care.