Lynny,
Can you post a picture example of the internet header? I am not sure where that is appearing in order to try and repro it.
Other things to add:
- The account that the Contacts are in is an Outlook Data File and is a .PST. There is no email account associated with this account. Not sure if that matters but it is not a MAPI account.
- If I copy one of the Contacts whose notes cannot be edited to a MAPI account with a Contacts folder, the Contact stays not editable.
- I am using Companion Link (DejaOffice) for syncing this account to DejaOffice Cloud. However, this is reproducible by copying an affected contact into any MAPI email Contacts folder, as mentioned above.
- I checked the contacts data from the same Account on another Windows 10 Pro PC running version MSO (16.0.11126.20192) 64-bit and there are no problems with editing any of the Contact's notes.
Contacts unable to edit notes
Contacts able to edit notes

Internet Headers Contents from first internet headers photo:
Return-Receipt-To: "Lynny Moore" <*** Email address is removed for privacy ***>
From: "Lynny Moore" <*** Email address is removed for privacy ***>
Subject: =?iso-8859-1?Q?#PMT_-_Make_a_Payment?=
Date: Mon, 20 Mar 2017 08:48:01 -0500
Keywords: Suppliers
Message-ID: <*** Email address is removed for privacy ***>
MIME-Version: 1.0
Content-Type: multipart/mixed;
boundary="----=_NextPart_000_0B18_01D33729.309D5340"
X-Mailer: Microsoft Outlook 15.0
Thread-Index: AQHdfoPNDEC8KqwGY9u4f9ag5ZuLzA==
Content-Language: en-us
X-MS-TNEF-Correlator: 000000000B2171****3061F32E4AA97A8B4EA97792B3
Disposition-Notification-To: "Lynny Moore" <*** Email address is removed for privacy ***>