In Harry's case in Death Mask it was a little more complicated than that. The mission from Heaven
was to keep Harry safe, yes, Shiro unknown at the moment was dying of cancer was willing to take Harry's place.
I'm not sure how the fact that Shiro was dying of cancer has an impact on the Knights' willingness to rescue people.
Let's use another example of the Knights rescuing someone: Ivy.
The situations are parallel. Both people were kidnapped through use of that giant pentagram, for purposes of forcing them to accept a coin. In both instances the Knights were not getting any holy bat-signals of where to find them, but believed that they could be found in other ways. In Marcone's case, they refused to go look for him, and in Ivy's case, they agreed to go look for her.
Differences between the two are:
1) Marcone's a bad guy, and Ivy's a good guy
2) scale of potential damage
3) by the time they went looking for Ivy, Harry had convinced Michael that Lasciel's shadow wasn't around to screw with him
I can't think of any others.
For 1, the Knights of the Cross aren't supposed to judge people, so I don't see how this should matter. You could argue that, per Skin Game, the Knights of the Cross have a special responsibility towards innocents, which Marcone was not. However, in context of when Michael said that in Skin Game, it seemed to mean that an innocent was someone who hadn't chosen to expose themselves to whatever danger, and since Ivy had chosen to expose herself to the danger of the Denarians when she agreed to mediate the dispute, she shouldn't count either.
For 2, Michael made it clear in Skin Game that the stakes of a single soul was enough to risk an archangel Falling, so the fact that Marcone's soul was in danger should have been enough.
That leaves 3 as the only reason I can think of for the difference.
Can other people think of other reasons?