How do I use a Dropdown 'Entries' Field Type in a Front End Form
Simply put, an Entries field is an array containing entry ids, and your form needs to send it that way.

Just replace name="fields[tbdDesignerUrl]" with name="fields[tbdDesignerUrl][]". That way the value gets submitted as an array.

Also replace value="{{ entry.designerUrl }}" with value="{{ entry.id }}", since we need the submitted value to be an entry id.