You can't "delete" a record from a layout, only from a table, but you can keep a record from being displayed on a given layout.
There are several options:
Omit Record. The records displayed via a given layout come from a group of records called a "found set". This could be all the records in your table or the group of records pulled up from your last "find". Omit record is an option in the records menu that removes the current record from the found set. This is temporary as your next find or Show All Records command will return the record to the found set.
Set a value in a field to mark a record as "returned". Script your finds to omit records with "returned" in this field. This is a bit tighter design and enables you to tell at a glance which records are "returned" and which are not. If the user performs a manual find, or Show All Records, they can still bring this record up for view. Script triggers can be set to automatically omit a "returned" record from the current found set should a user attempt to view the record from this layout.
Set options in manage | Security that keep all records that are marked "returned" from being viewable by anyone who logs in with the same privilege set as your receptionist does. This is much more secure but takes more work to set up. If you log in with different credentials, you'll still be able to find, view and edit these records.