In the custom record setup, the record will be inline editable from the parent record if the ‘Show Remove Link’ and ‘Allow Child Record Editing’ boxes are checked. In that case, there will be a “remove” link in the custom record sublist view.
To avoid this link from the list, make the parent field mandatory in the custom record. There will be a parent link field in the custom record. Make that field mandatory and the remove link will disappear.