Administrator Suggested Tiles can be edited or deleted like any other tile on the Personal Page.
Changing the name, title, description, and color of the tile will retain the connection to the original Administrator Suggested Tile. When the administrator updates the tile, the tile on your Personal Page will be updated accordingly. However, if you change the configuration of a tile (such as when you change the search criteria for a Custom Query Results tile) or delete the tile, the connection to the original Administrator Suggested Tile is broken. When an administrator updates that tile, you will receive a new tile with the new configuration and, if it hasn't been deleted, the tile you originally edited will remain on your Personal Page.
Changes you make to Administrator Suggested Tiles on your Personal Page do not impact other users.