Trehalose is a natural sugar with two glucose, similar to maltose but with different linkage. Some people who have fructose metabolism issues like it for that reason. It doesn't seem to be too widely available on its own, but Swanson Vitamins sells it in small containers and it tastes great IMO. Rice syrup is mostly maltose.
All c. difficle can metabolize trehalose, but the two strains in question have different adaptations that allow them to metabolize it when present in lower quantities.
If this is confirmed, I'm guessing that the implication is less about avoiding trehalose normally but avoiding larger quantities when taking antibiotics. Maybe people on anbitiotics will also be given trehalase enzymes to take with meals. In general, taking a wide varity of digestive enzymes and avoiding prebiotics and excess sugar when on antibiotics might be a good idea to limit the energy available to resistant bacteria in the colon (or maybe not, it looks like there is some evidence that taking some forms of sugar with antibiotics improves the effectiveness of the antibiotics in some cases).
It is a seperate consideration if this is contributing to the overall increase of c. difficle or if it is just determining which strains are more common.
Expect to see a lot more "food X causes undesirable microbiome effect Y" research in the future as more of this kind of research takes place.