For my first two TMD's I made bins to hold the various tiles.

For TMD-3 I decided to take advantage of the fairly strong magnets in the tiles so I designed a grid to hold the tiles and ordered some sheet steel to mount behind the grid to attract the tiles.

Well live and learn. I discovered that the steel I ordered was Austenitic Stainless Steel which is non-magnetic. Fortunately it was not a costly mistake and I'm sure I'll find a use for it in the future. So my plan B was to order a small cheap magnetic white board. Much better. After removing the cheap plastic frame and cardboard backing I had a nice flat magnetic backboard.

I cut the metal sheet to size and, using a CA glue, mounted it into the tile organizer frame that I printed.

Similarly I glued in the tile organizer grid.

And here it is with a set of tiles installed. 

The magnets hold the tiles in place nicely. You can flip the frame upside down without the tiles dislodging, yet they are easy to remove when needed. I like the coordinated look of the TMD-3 and tile organizer.