Hey there, Kyle!
Thanks for stopping by the Apple Support Communities.
The error message you are receiving indicates some contacts on your iPhone are read-only. This means you can view them on your iPhone, but not edit (or delete) them. There could be a few reasons for this to occur, and more than one path to troubleshooting the issue given that. Let's start here:
- If you have synced contacts to your iPhone from a computer through iTunes (or Finder on a Mac running macOS Catalina or later), you can only remove the contact by going through the sync process again. Steps do that can be found here: Sync iTunes content on PC with your devices - Apple Support
- If your iPhone has a configuration profile on it, used by an employer, school, or other such organization to manage your iPhone, you will want to speak with the IT administrator at that institution. It may be that they have purposefully prevented some contacts from being removed from the iPhone. You can get more information on profiles here: Install or remove configuration profiles on iPhone - Apple Support.
- If you sync your contacts through an account other than iCloud, like an email account, you may need to remove the contact from its origin account. For example, if you have Gmail contacts syncing to your iPhone, you might need to log into the Gmail.com webpage and edit the contacts there. You can test this by turning off any other accounts that might be syncing contacts to see if the one(s) in question disappears: Use other contact accounts on iPhone - Apple Support
Don't hesitate to respond back if the issue is unresolved after that.
Enjoy your weekend!