With SalesAnalysis 9.3A (2020.01.28) I could not replicate running Set Paid Invoice Indicator and see the Invoice Date of an already retrieved invoice get changed from one date to another. I tested with sample data, and all transactions and running set paid invoices on different login dates, to track. Invoice, cash and credit note. I posted the invoice and credit note through OE (9.3A, 2019.11.25)

Since you can replicate, please provide succinct steps to replicate. Please indicate the settings selected on Set Paid Invoices when run. If there is a problem here, it is more than just posting a credit note with a different date and retrieving into SalesAnalysis, then running Set Paid Invoice.