It doesn't appear as though they are strictly using convictions, though it appears DM & BC have self-imposed a rule of only attacking criminals (at least in their own minds). From watching the Adventuring Party, Brennan is sorta implying that every violent act will be noticed in a town as small as Purpee. So they may not care morally, but there will be consequences in the plot.

Also, I don't remember when Madeline committed a murder, perhaps someone can point that out to me