Can I put tile in my basement over Ditra and existing mastic?
Schluter may not warranty Ditra if your slab does not permit moisture and you use a modified thinset.

Laticrete Stratamat has a "mortar hydration vent" that is claimed to allow either modified or unmodified thinset.  I have found significant price breaks for Stratamat if ordered online.  Local suppliers are a bit higher, but sometimes worth spending extra for "I-gotta-have-it-now" moments. 

I would do an experiment with a modified thinset and a couple of cheap tiles...  Test adhesion at 12 and 24 hrs..  Use the std. Rockford chisel-and-3-pound-maul shear test...(wear goggles).