Demolition: Luon and polymer composite whatever tile
This is self-explanatory. I stood on this stuff, grabbed it, bent it, leaned my weight on it, and it just went WOOP WOOP WOOP and wobbled around like an Australian man playing a saw (there's an old Australian man lying, dying...).
This is the only way I've found to do it. Brain-dead easy, just anchor your foot down and give one gentle pull.
Man, I can't carry a full bag though. This stuff's heavy!
(And yeah, the subfloor's structurally sound but not a good substrate for Ditra. Going to lay another 23/32 tongue and groove, both for a good substrate and to deal with some weak spots I've unscientifically discovered by divining the material density and tensile strength.. I want that floor uniformly strong)
If you can't explain why, then you don't know what you're talking about. I'll keep asking until I find someone who does.