Simple. Because we're trying to make this feel like a proper, well-connected franchise with good continuity. At present, we have American accent Moira in the CIA and, 30 years later if we accept X1-X3 were in the 1990s, we have Scottish accent Moira at a medical/science facility that we could easily assume was intended to be Muir Island.
If they're trying to connect the dots, then she could have a small part in the story, either in this film or the next. It's not absolutely vital but it would give the franchise a more cohesive feel if they gave an arc from First Class Moira to X3 Moira.
We don't know exactly how much was erased from her mind but, even if she can't recall the location of the mansion, it wouldn't be difficult for the CIA to find the Charles Xavier residence!