How do I change or eliminate the flower on the upper right corner of my emails in Mail?

But I learned something new.

I think I did, also.

If your in an Open Directory environment then Mail may use icons associated with user accounts. Actually to be more precise what is happening is that Mail uses Contacts to both auto-complete addresses and also obtain icons for users. Contacts may do this as per this discussion for your own personal address card and personal cards for your contacts but can also be connected to Open Directory and hence find icons via that. Kerio Connect (a Mail server) also supports storing and providing icons for the accounts you define on it. In the case of Kerio Connect the Mac Contacts application can 'find' these pictures by adding a CardDav account in Contacts that links to your Kerio Connect server.

Contacts may also cache icons for accounts, possibly in the following locations.

~/Library/Application Support/AddressBook/Images

~/Library/Application Support/AddressBook/Sources/[UUID number]/Images

It is also possible to install a plugin to use with Mail so that it can find pictures for other users and label your emails with your own picture so that your picture will show up on other peoples computers if they have something similar installed. See https://www.feingeist.io/mail-plugins/#Face2Face

Also see https://en.gravatar.com/

Mozilla Thunderbird can have an extension installed to do the same thing. See http://blog.gravatar.com/2010/08/24/thunderbird-extension/