A custom URL is set after creating the record, and cleared with an empty string

• Setting it: a custom URL is set after creating the record, with {"customUrl": {"url": "/campaign"}} on its edit route; check fullPath in that answer to confirm it took effect.
• Clearing it: send an empty URL, {"customUrl": {"url": ""}}.

Start the path with a slash: it is stored exactly as sent, and one without breaks every link built from fullPath. A URL another record already holds is a 422, "This value is already used."

See Set and clear a custom URL through the API and Custom URLs and slugs.

In the API reference: Edit a page.