Paradox Brothers
The squad became famous for screwing up missions of countries not allied with Grass country. Examples include giving away the position of ninja trying to hide, protecting the target that is supposed to be killed, and killing the target before the assigned team does then going to the village leader and asking for payment. The squad members are called Kyoke (The Fool), Mitsuke (The Clown) and Kotsukei (The Joker). The Joker died shortly after the squad was created. It appears he was actually an old man and somehow used a genjutsu to trick anyone, even with Issekigan, to see a young adult rather than an old man. Since he was the leader the squad hasn't been active lately.
When joining, the new person has to be branded with the kanji for whatever position he is filling in (fool, clown or joker). The brand usually goes on the right hand. After branding, a special liquid is pored over the person's hand (which stings even more). The branding is actually a seal which makes it impossible for someone to infiltrate the group. The seal gives the group telepathic communication (so they can sense when the other is in danger and whatnot). They can also share what they are seeing/hearing with each other. The telepathic communication is private, only to the brethren of the group (no outsiders can penetrate/compromise it). They are also able to read each others minds. This makes each member of the group tightly connected to each other, which is why they call themselves "brothers." Apparently, the connection does not become noticeable (to the new member) until a while after the branding.
The squad has been spoken about for a long time. Sometimes when a mission goes wrong, people will blame this group, which is considered a joke and a myth. Each person wears a mask that symbolizes which "brother" he is (fool, clown or joker). It is believed that the squad was started by some Grass ninja because it only targets enemies of Grass country. The squad may be based off of Paradox Project.
Later it is revealed that the first Kotsukei (Joker) really was from Paradox Project. He joined them late in their development and he was soon the last one left from the project. He was the last to have the Scroll of Paradoxes but got rid of it and lost it because he couldn't understand it. Kenro (who is Mitsuke) realized that the Kotsukei must have been using the Age Paradox to look younger than he really was. Kenro was surprised that this jutsu was able to fool Issekigan. Kenro then deduces what his squad was really all about. Kotsukei, the creator of the squad, didn't create it to screw around with other countries. He created it to find the scroll again. Eventually he must have completely lost it and that's how the whole "screw up everyone else's missions" came along.