Flooring Tile - Porcelain tile over concrete.....with wood inset

Hi all. Was wondering if anyone can help me with a tiling question. I am installing 18" x 24" porcelain tile in my girlfriend's condo bathroom and have discovered that under the vinyl flooring is a concrete subfloor with the exception of the area under the toilet flange. The flange is installed over what looks like a 2" x8" x 20" piece of lumber inset into the concrete. My question is how do I tile over both concrete and wood without having to install hardiboard over the entire floor?

Is this for sure concrete or is it gypcrete?

I'd make sure everthing is flat and use a ½x½ trowel, with a modified thinset.

This would also be a pefect candidate for Schluter DITRA.