I found very useful article https://www.rackaid.com/blog/hotmail-blacklist-removal/ which advises on how to proceed with Outlook/Hotmail removal.

This article is for Dedicated server or Virtual private server owners
, normal users and shared hosting users need to contact their hosting providers.

ISSUE:

Example You or your client sent an e-mail to the [email protected] (or other Microsoft mail/hotmail/live/msn) from the domain hosted on your server (example: [email protected])

From: [email protected]
To: [email protected]

And e-mail was not delivered, because following error e-mail bounce back:

This message was created automatically by mail delivery software.

A message that you sent could not be delivered to one or more of its
recipients. This is a permanent error. The following address(es) failed:

[email protected]
host mx1.hotmail.com [65.55.33.135]
SMTP error from remote mail server after pipelined MAIL FROM: SIZE=3606:
550 SC-001 (COL004-MC6F16) Unfortunately, messages from 1.2.3.4 weren't sent. Please contact your Internet service provider since part of their network is on our block list. You can also refer your provider to http://mail.live.com/mail/troubleshooting.aspx#errors.
1.2.3.4 being the IP address from which e-mail was sent (your server / mail server IP)
As Microsoft hotmail says, they block server from which you sent e-mail. If server is not yours, contact your hosting provider. If server is yours, continue reading on how to proceed:

How to fix/get unblocked by the Outlook/Live/MSN/hotmail?

1. Discover which SPAMmy e-mails were sent and from which website/script it was sent out of your server. If you have Linux server, you may try googling: SPAM Linux mail server logs path; discover SPAM source Linux server

2. Prevent SPAM to happen again. Apply mail sending limits per time period. Try to use SPF, DKIM, DMARC measures on your server.

3. Check your mail server / server IP on the blacklist checks like: http://www.blacklistalert.org/ and make sure it is removed

4. Check https://www.senderscore.org to make sure your sender score is preferably above 80 for your server IP, no need to register, no big benefit

5. Verify your mail / MX settings and also other important DNS are bug free using tools like http://intodns.com ; http://www.dnsinspect.com

6. Ask Microsoft to remove you from their blacklist by taking time to properly and carefully fill the form at https://support.live.com/eform.aspx?productKey=edfsmsbl3&ct=eformts&wa=wsignin1.0&scrx=1