Hi Rachel,
You would need to proxy the basemap (embed your AGOL credentials) in the basemap item in order to avoid this prompt. Do you, or someone else in your organization, have ArcGIS Online credentials you can use to do this?
You would take the URL you posted and add as a new item to the Portal from the Content page. During this process you can check a box that you want to add credentials to the item. I hope this helps!
Regards,
Colin