How do I remove my mother's Apple Account from MacBook Pro?

Hello all,

After using my mothers Apple ID to watch some movies she had bought with it, I wanted to remove her Apple ID from my Mac.

It appears to be logged out, yet I keep receiving this notification. The alert pops up quite frequently and has been going on for a long time.

The notification I keep getting on my Mac is: “Mac cannot connect to Apple Media Services because there is a problem with ‘mail@gmail.com’. Open Apple ID settings to fix the problem.” It appears frequently and has been going on for quite some time:

When I click the blue “Apple ID settings” button, I am asked to sign in with my mom’s Apple ID. I’ve tried logging in with her Apple ID, but it doesn’t solve the issue:

I’ve tried to figure it out without success, but I’m hoping you can help me get to the bottom of it.

The pictures attached are the notifications, which are in Norwegian, but might help to show you what the issue is.

Thank you in advance!

[Edited by Moderator]