If you’re using only using the project management and time tracking functions of Paymo but use another software for accounting and invoicing, you should set up your projects as non-billable.
If you want to keep track manually of billed & unbilled time you can set up billable projects and then you can mark time entries as invoiced by going to Timesheets → Agenda view → select a time interval, check the desired entries, and click on the Mark as invoiced button.