According to the REST API docs, the tile has a parent which points to the place: https://developers.jivesoftware.com/api/v3/cloud/rest/TileInstanceEntity.html
A Tile Instance is a component of a purposeful place associated with a Tile Definition for displaying data from external services.
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You can use the jive.tile.getContainer function as described here:
The callback function gets the place object as an argument. I believe it contains the URL, but if not, it should at least have the id.
Hope this helps,
Thank you for your help, Scott. This worked as expected. The returned object contains both the placeID and the URL.