I had a friend play this tonight when we were playing the second scenario of Forgotten Age, and he had a pretty clever use for it: he took the last clue off of a high shroud location (shroud 5) and put it on a slightly lower shroud location that had just been revealed (shroud 4). Why was this clever? Because the location we took the last clue from was worth a victory point.
Now, you can obviously use this card to lower the shroud of a location and make it easier to investigate for a turn, but I don't think that's terribly relevant. Why? Because, except for a few corner cases where people have extra actions, you are, at best, going to get two investigations with -1 shroud.
I think the best use of this card you are going to regularly get to use is taking clues from locations you don't want them and moving them somewhere else. And I don't just mean from high shroud locations. Some locations inflict a penalty for trying to move on to them or for trying to investigate on them. And I can think of three locations from that scenario alone that would fit the above description.
But the times you will be most proud of yourself will be the times when you spent one resource and net your team a victory point.