More sad news. While they managed to disable the Safe Links feature on my account, there still exists their safety tips feature. See:
https://www.petri.com/exchange-online-protection-safety-tips
https://support.office.microsoft.com/en-us/article/Enable-or-disable-safety-tips-in-Office-365-f09668bd-fe1a-4c01-89e3-e88c370e66c7
Their Exchange server will add tags to an e-mail that triggers the client (Outlook 2016) or modifies the content of an e-mail (for other clients) to insert "mailtips" of varying alert
levels. Yep, more modification of e-mails. Sometimes when I attempt to reply, OL2016 would interfere by refusing to let me reply until I click on an infobar warning be about a /potential/ phish e-mail. On those flagged e-mails, I have to click on the infobar
to allow the content (links) before I am allowed to reply. There is no setting within OL2016 to disable this, um, feature. Peculiarly, their Exchange server was flagging e-mails from their Outlook support team (who disabled the Safe Links feature) as a phish
e-mail. Hoisted on their petard.
Users of school or corporate accounts can go to https://protection.office.com to
disable both safe links and safety tips. That is not an option for users of free Hotmail/Outlook.com accounts where changing policy settings in an account must be requested to and performed by a sysadmin.
I've submitted a request for them to disable EOP (Exchange Online Protection) on my account, specifically the safety tips feature (safe links already got disabled). No way for me to test if they accomplish that request since getting interfered on replies
with a warning about a potential phish e-mail is erratic. Those e-mails do not get moved into the Junk folder. They are delivered in the Inbox folder but with a red safety tip that they might be phish e-mails. That I no longer see the mailtip could mean
they disabled the safety tip EOP feature or that their Exchange server has yet to detect another incoming e-mail as a phish candidate.
I have a Hotmail account and that's the one they, so far, have disabled the Safe Links feature. Hopefully they will also disabled the safety tips feature. I have an Outlook.com account so, oh joy, I get to submit the same requests over there, too.