User wants to limit the options on the Submit Time dialog so that the employees can submit time to a specific person only.
As of now, there is no way to limit the options on the Submit Time dialog. However, it is possible to hide the dialog for the employees using security permissions so that when employees submit their time entries (or expense entries), they are sent to the specific user set for them by the CORE Admin. You can do this by first setting the default Submit To option for the employees on the Employees > General > Rates & Options screen. After that, you need to un-check the security option Show submit options when submitting time entry under Security > Time Entry of that employee. Now when the employee submits time, CORE does not show the Submit Time dialog, but rather submits the time automatically to the default Submit To person set for the employee. A similar security option is available for expense entries. Check CORE Help Center for more on how to customize security permissions.