To delete a link to another record:
If you wish to remove both the Text box and a non-relationship Element from a record, use the 'Delete an Element' option instead.
If you wish to remove only the contents of the Text box of the non-relationship element, use the 'Delete the entire contents of a Text box' option instead.
But do NOT use these other deletion options, when a text box contains a link. If you do, then these options will delete contents of the box, and the link from the record to the other record, but will not delete the back-link in the other record to this record.