Each Grantee should have a Primary Grantee Contact. Most frequently, the grantee profile is its own primary contact if there is a name associated with the grantee on the Profile 1 tab. However, it is possible to have no profiles as primary contacts and for the grantee to also not have a profile 1 name. In this instance, there is no primary contact person.
If you want to delete the current primary contact person, you might want to assign another contact person to be the Primary Contact person by clicking the primary box when their name is selected. After saving the record, they will have become the primary and you can click the "x" to delete the old record- or retain it but not as the primary contact.
When adding a new Grantee profile with a Profile 1 first and last name field filled in, the primary contact person record will automatically be created as the grantee profile. If there is no first and last name, the contact persons tab will remain blank.