How to remove people from search in mail app?
I don't think you can remove the people list from search results.
If you search, for instance, for "Service Desk", mail will lookup in any header: From, To, Subject, and other; therefore mail will include previous recipients and contacts.

Solution 1

Be specific about the message header to use in the search.
You can perform the search by adding the keyword "Subject": Subject: Service Desk

Solution 2

Create a smartmailbox like the one in the picture.
In this example the smartmailbox will lookup for all message containing the word "Facebook" excluding this word from sender and recipients.
You will need to double-click the smartmailbox and edit it every time you want to do your custom search.