This is Working as Designed. If the billing statement option 'Include Procedures with Claim Pending' is checked then the Billing Statements will show all associated procedures codes (regardless of the date) on all pending claims (which have not yet been paid) at the bottom of the Billing Statement with an asterisk signs (*) next to the pending claim's procedures.
The * sign is indicating that the procedure codes have been billed to insurance and are unpaid claims. This option to 'Include Procedures with Claim Pending' is simply a visual preference and you do not have to have the option checked, it is an option of preference, so if you uncheck the option the procedures on pending claims will not be shown at all as this turns the feature off.
However if the option is turned on, then once a payment is made you will need to wait until the next month's billing statements and then the associated procedures will be omitted from the statement. Or optionally, you can change the Balance Forward Date in Office Manager Reports Billing to a date that is AFTER the payment date.