FAQ after you've been discovered to be the culprit in the case you invited the detectives to

Q: How did you figure it out?
A: It was elementary, really. We discovered patterns of shoes in the mud that matched a male size 9, and by the depth of the imprint we were able to conclude that it must have been a male between 180 and 184 pounds of weight. Looking at the distribution of the weight, we deduced that the interloper was able to 'run back' from the window, so to speak, to make it look like they had run INTO the window, while in reality, they were an insider, pretending to have been a stranger.

Q: What now?
A: You see, since we're not the legal authorities, we don't have the jurisdiction to arrest, or conduct any legal business. We are not law enforcement authorities, neither are we associated with the government directly. However, we can make moral judgments on the nature of the events, and prod the correct persons towards the actions we feel would be most suitable. In this case, it is clear that the Bobbies will be unable to identify the real culprit, and will be on the lookout for a very short stranger who ran in and out of the house. For our case, that is perfectly fine. However, if in the future you were to pretend to have lost your valuables for insurance fraud purposes, we must warn you that you will be summarily reported, not just for the future crime, but this one as well. Additionally, now, to put it in the modern parlance, you owe us one, and will need to give us a big one, at any point of our desire, likely at a crucial point during a future case. Ta!

Q: Do we actually need to pay you etcetera?
A: Yes, since you were so overconfident of your abilities to fool the authorities that you not only called the bobbies but also hired unofficial detectives (us), you will most certainly need to pay us, plus the extra thirty percent hush money, if you don't mind us saying so. Maybe send the hush money to some children's hospital or orphanage, whatever, under our name, so that they will owe us one as well. If you really think about it, we're running one massive pyramid scheme of favors.