Hi @Patti_R,
Deleting all records the emails are logged to would be one option, yes (contact records and your company record, otherwise emails might still be kept on the company record).
Alternatively, navigate to the email index page (Menu > CRM > Contacts > click blue Contacts dropdown in top left corner > change to Email).
On this email index page, you can set a filter for Associated records – and select the contacts for whom you want to see logged emails, then bulk delete them:
Best regards!