If you use Sync then best is to disconnect Sync temporarily during troubleshooting.

This could be a problem with the places.sqlite and favicons.sqlite files in the Firefox profile folder.

• use the "Places Database" -> "Verify Integrity" button on the "Help -> More Troubleshooting Information" (about:support) page

If errors are reported with "Verify Integrity", close and restart Firefox or reboot and retry.

If "Verify Integrity" cannot repair places.sqlite, rename/remove all places.sqlite and favicons.sqlite files in the Firefox profile folder with Firefox closed. Firefox will rebuild places.sqlite and restore the bookmarks from the most recent JSON backup in the bookmarkbackups folder.

• keep a backup copy of places.sqlite in case a new places.sqlite database has to be created
• you lose the history when a new places.sqlite is created

You may have to restore an older bookmarks backup in the bookmarkbackups folder via the Bookmarks Manager (Library).

• Bookmarks -> Show All Bookmarks -> Import & Backup -> Restore
• https://support.mozilla.org/en-US/kb/restore-bookmarks-from-backup-or-move-them

See also:

• https://support.mozilla.org/en-US/kb/fix-bookmarks-and-history-will-not-be-functional
• https://support.mozilla.org/en-US/kb/cant-add-change-or-save-bookmarks

You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

I followed the support suggestions up to the point of successfully running Verify Integrity which apparently fixed an error in the Bookmark lists that may or may not have been part of my problem.

The four URLS that at first could not be removed were all in the Bookmarks Menu (not in the "ToolBar") and had been Imported from an ancient version of Safari (> 10 years ago) that I used before Firefox. The URLs apparently dragged along all the Cookies that were installed years ago before internet security was a major issue. Those cookies apparently were locked to assure permanent connection of those sites to my computer and therefore could not be removed using just Remove Bookmark. After running Verify I followed up by a power off, complete rebooting. Finally upon suspecting that "evil" cookies were involved, I erased all cookies gathered at startup and in response the Mac OS 10.15.7 system apparently made copies of the offending URLs and placed them at the top of the Library listing where the delete command (rather than the usual remove bookmark) was available. The application of delete to each of the four links effectively removed all trace of them. If the instructions about finding and running Verify had not been provided by your support person, I probably would still have those "bad" URLs hanging around somewhere. Thanks.