They should still get the mission specific reward, but what the consequences of them failing are depends on how badly they failed
If you are going by the book on this faction mission, the Harpers have already gotten a recommendation from a long time member to
recruit the doppelgängers into the Harpers.
They have told the characters :
[...] We need an unbiased opinion. Track down and speak with each of the doppelgangers, and gauge their trustworthiness.
i.e. they want a second opinion on a group that has already been verified by a long standing member.
The DM text of the specific faction mission contains the following detail:
The characters must speak with five doppelgangers, starting with their leader, “Bonnie,” who works at the Yawning Portal.
Characters must interview each doppelganger and succeed on a DC 16 Wisdom (Insight) check to ascertain its trustworthiness. Only “Bonnie” is trustworthy. Reward: Each Harper character gains 2 renown. Every contributing party member receives 50 gp.
So, the character should get 5 chances to ascertain trustworthiness, one for each
If more characters get involved, each could potentially get a chance to ascertain trustworthiness for each
interviewed. Your question suggests you only gave your players one chance for the group...but I may have gotten the wrong end of the stick there.
It's important to note, failure to ascertain trustworthiness or untrustworthiness doesn't necessarily mean the character believes the opposite of the truth. It also doesn't mean they have "failed" the mission and don't get paid.
For example, after interviewing
the character makes a DC 16 Insight check to ascertain her trustworthiness. They get a 12. As the DM you now have two choices:
- The character is unable to ascertain trustworthiness (i.e. she is hard to read)
- The character believes the opposite of the truth and believes that
Which of those options you assign to the PC will affect the failure state of the mission.
Their task was to ascertain trustworthiness. The Harpers don't necessarily already know the truth of the matter, that's why they want a second opinion from someone who has been in their organisation for a while.
If the character doesn't identify the untrustworthy
and as a result they are admitted to the Harpers, the price of that failure to identify untrustworthiness may not be felt for years.
For example the untrustworthy doppelgänger admitted may, bide their time and at some point in the future replace Mirt. At that point the doppelgänger has gained a significant amount of control of the Harpers and is a Masked Lord to boot! At that point their failure is immense, but by then there may be nobody around of sufficient rank to care.
Alternatively it may be found out immediately
The untrustworthy doppelgänger may be admitted, and betray the Harpers on their first a relatively unimportant mission but be found out. In this case the failure state of your PCs mission is small.
A note might be made not to assign "character verification" type missions to that PC in the future...if it's noted at all.
The immediate reward for carrying out the mission should still be paid to each participating character. They did what they were asked to do, they may have been wrong in their conclusion...but they still did the assigned task.
Note: my experience for this answer is that I've DMd the full campaign of Dragon Heist, and while I haven't run this specific faction mission, I have given my players others where the failure state of the mission is...unclear.