On my 2003, I have a similar cup holder tray but it is not exactly the same. It is held on with two screws with large washers that screw through the tray into the doghouse. If you remove the doghouse, you might be able to see the ends of the screws (unless they are covered by doghouse insulation) protruding into the doghouse. If they are covered by insulation, you might still be able to feel for the screws. Can you lift or pry out the black pieces from the tray to see if there are any screws underneath them?
2003 Itasca Sunova 30B towing a
2010 Cadillac SRX