If you want to change the bill rate of a time entry without changing the employee bill rate or the rate specified in the fee schedule, you can do so from the Time Entries screen itself as this is the rate that CORE finally uses on the invoice. You can also use the Actions > Update Rates option there to do that. Check CORE Help Center for details on Update Rates.
Another way to do this is to change the bill rate when creating the invoice. For that, in the Create Batch Invoice screen, click T&E Details on the grid for the billing record. On the Time Details tab, change the bill rate for the time entry and click Save. The invoice uses the updated rate for the entry.