The mugger is a Deontologist in this scenario and therefore does not lie. If the utilitarian couldn't trust the mugger's promises, the whole scenario would fall apart as they couldn't trust the mugger's promise to cut off their finger.

How does the utilitarian know this?

Any morality needs to take into account our uncertainty about claims other people make.

The mugger has a lapel pin denoting himself as a deontological agent. Lapel pins in these fantasies cannot be forged, I guess.

If we're assuming unforgeable moral-method pins I don't think we should expect intuitions generated in this sort of thought experiment to be a good guide to what we should actually think or do.

The mugger is a deontologist, right? We're already assuming that he'll keep his promises.

I mean, he's a mugger. Clearly doesn't take his deontology too seriously.

But notably not threatening or committing violence toward anyone else!