How to remove Microsoft items from Background App Activity list?

The short answer is no, it is not possible to manually remove items from that list.

The list of items in System Settings > General > Login Items & Extensions cannot be directly managed by the user. The list is populated by macOS based on what apps have requested to run in the background. The user can enable or disable apps allowed to automatically run in the background, but you cannot remove items from the list.

As you can see in your screenshot, the settings pane does show apps that are currently running in the background, not running, etc. One status listing not present in your screenshot is 'last ran in background n days ago', you can see that under the Microsoft OneDrive item in my settings pane.

More info: Manage login items and background tasks on Mac - Apple Support

Item will eventually fall off the list if they are completely removed. The bottom one on my list, QNAP Systems, is for an NAS that I used to have before I switched to Synology >2 years ago. I deleted the app but when I use EasyFind (which searched hidden folders), I see that there is still a QNAP folder and a preference file in my Library folder.

It is best to just ignore the items on the list. Leave the toggle OFF for things you don't want running or that have already been deleted from your Mac.

Since you mention Microsoft, they do provide instructions for completely removing MS 365, including deleting items from the Library folders.

https://support.microsoft.com/en-us/office/lifecycle/officeinstall/uninstall-office-for-mac

thanks for the reply. i did remove all of my ms stuff as you had indicated. i can live with it, but wanted to clean up the list. regardless appreciate the feedback.