I've just been to look at a floor which has half quarry tiles & the other half a nice & flat screed. They have ordered travertine. Kitchen will have new units fitted.
The thing is, the tiles are stuck down well, & are perfectly level to the abutting screed, so would it be just making things worse by lifting them all up, plus all the extra work & cost of getting it all level again, when its all nice & level & solid to start with. Would you agree that as there is no heated screed & its been down a long time anyway that there is no need for a decoupling membrane.
before you consider tiling, get a moisture meter on top of those quarries, and check for moisture, if it's too high and it's an old house, the quarries will propably on top of cement thrown down on earth with no dpm, in which case you would have to latex screed over the quarries and the existing screed, apply an epoxy dpm then use a spf adhesive on top of the dpm which can be tiled directly onto, provided there are no pin holes, and the manufacturer of the adhesive allows it.
Latex screed is quicker and easier to use than adhesive therefore costing less in labour in the long run, but, as Dave said, you can just Ditra straight over, just make sure that any wax or oily product is stripped out of the quarries beforehand, in case the adhesive doesn't bond to the surface, in all cases the quarries will need to be primed initially and solidly fixed to the substrate.