Using classic Outlook for Windows in business environments
I understand your frustration when a job need to be done, it has to be done.
Your Outlook App is probably in off line connexion mode. This prevents outlook from doing the delete contact operation that you need.
You will have to put your Outlook appl. into a 'non-off line' connexion mode.
To do so...
In the outlook appl Click on the E-Mail Icon on top left of your screen (the first Icon under the OUTLOOK title)
This will give you access to your Email general environment.
Move your mouse pointer over your E-Mail address and 3 dots will appear (...).
Click on those 3 dots.
A popup menu will appear. Click 'Manage Account'.
On this new panel, click 'General'.
A new panel of selections will appear.
Click the 'Off line connexion'.
There you should find a toggle button (activate off line connexion) if it's Blue (activated) meaning that your system is in a Off line Connexion mode.
Disable this toggle button by clicking on it once. This will change from blue to grey.
Exit this pannel. Go back to your contact for this E-Mail address.
Select the 'People' icon on the left handside. Select all contact menu for your EMail name.
Select one Contact in your list as a sample test and Right click mouse to 'delete' contact.
This contact should be remove from your list.
Hoping this will work in your environment.
It did work on mine.
Good luck.