Hi Joseph Pollone,
We understand you're trying to remove an email address suggestion from the iCloud website. We're happy to help.
Now it looks like that email address may be assigned to a contact since the full name "Barry Green" is showing to the left of that email address. If you have this person saved as a contact, aside from selecting Remove From Recents, you would also need to delete the contact.
Remove email address suggestions in Mail on iCloud.com
If you have any other information saved to that contact like a phone number or other email addresses, make sure to jot that info down before deleting the contact. Once it is deleted, you can then create a new contact for that person. After those steps, check to see if it is still suggesting this email address when you try to compose a message.
We hope this helps. Take care!