Thank you for adding a post here in the Community, @amosdepuy.
To close your open invoices, there must be a payment link to those invoices. It's my pleasure to help you how.
The reason why invoices still show as open even if the customer/s paid those invoices, is when you've entered the payment as Bank Deposit or a Journal Entry instead of a Receive Payment. In this case, the payment wouldn't be linked to the invoice and the invoice will remain unpaid.
If you've entered the payment a bank deposit, you'll need to edit the deposit. To find the deposit entry, check your bank register.
If you've created a journal entry, you'll need to apply the journal entry credit to an invoice.
I've added these articles for additional reference:
I'll be right here to help you if you have any other questions about handling open invoices in QuickBooks Online. Wishing you the best!