Lois Green wrote:
That has nothing to do with Contacts app. These number are stored in the Message app cache and there is no way to clean it up unless you restore your iPhone as new. But if you restore your iPhone as new, you will lose other files on iPhone. And if you then restore iPhone from iTunes backup or iCloud backup, you will get back contacts
While that was true when the OP posted two years ago, it no longer is. In the intervening years, Apple has added a way to remove people from the recents list that shows up when you message people. If the contact has been removed from your Contacts but still pops up when when you start typing in a name in the To field in messages, it will have an "i" in a blue circle to the right. Tap on that. Tap "Remove". Confirm Remove from Recents.