The data reported from TimeCard Single gets sent into a Access database which is placed under My Documents\My TimeCard. You can see all data there and in the Excel statistics reports, but the easiest way to get data for invoices is probably to generate Excel reports from the Reporting dialog.
In the TimeCard Settings, Other Settings, select to group the data by customer in the Excel report. Then open the Reporting dialog, set the time period you want to include in the Excel report and get the values.
Now you can review the data and change it if needed before you click on the Excel button to generate the report. In the report, your hours (and expenses if you are using that feature) will be summarized by the customer.