There were two issues with the step.
First issue was to remove the glue used to hold down the original rubber mat (which was shot). I used paint stripper and scraper; the old crap came right off. It was nasty. I'll post a picture of the completed step later. (BTW, Lowe's carries a nearly identical rubber grooved matting material at $2.50 per linear foot, 24" wide).
Second, one of the step ends needed replacement since the particle board had been busted off (yellow circle). I used 3/4" MDF since it's all I had on hand, and ran a groove for the new T-Molding using a table saw with a 1/8" blade. The groove width is wider than ideal for T- so I'll need to secure the molding with hot glue, but this seemed like an adequate solution considering I did not have a T-Molding saw (if such a thing exists). Using a table saw freehand for this purpose is a bit tricky; watch your fingers.