A situation came up with these cards:

Quaithe of the Shadow + Blood of the Dragon attached, and Maester Cressen.

Is it possible for the Maester to remove the condition, or is it impossible to remove since Quaithe becomes immune to character abilities?

Well,  the Qaithe of the shadows immunity to charachter abilities won´t protect the attachment from Maester Cressen´s ability.

So Maester Cressen can legally discard the attachment blood of the dragon. 

 Some points of clarification on this.

Note that Quaithe's ability makes it so that opponents cannot choose her as the target of events or character abilities while she has an attachment. That is not the same thing as immunity, which is a separate game term. An event or character ability that affects her without choosing her as a target (like, say, Westeros Bleeds) can still "do stuff" to her. If she were immune, she'd ignore everything, target or no. (That particular point doesn't factor into the specific example of Cressen going after the attachment, but it is an important distinction for the scope of her ability in general.)

Also note that since her ability only stops herself from being chosen as a target, it doesn't extend to cards attached to her or other characters around her (say, if she were participating in a challenge with Khal Drogo). So the key here is to look at WHAT the event or ability (in this case Cressen) is choosing. Since he specifically chooses (then discards) the attachment, you do not run afoul of Quaithe's ability. She is only protected from things that specifically choose characters.

thanks for the replies!