The Thunderbolts were formed by Helmut Zemo, who sought to create a team of supervillains powerful enough to defeat the Avengers. Over time their purpose has changed and now we're left with supervillains that want to redeem themselves by doing some good. The latest incarnation of the Thunderbolts was led
by none other than the Winter Soldier. He re-established the team in order to stop S.H.I.E.L.D from using pieces of the Cosmic Cube to reshape reality.
Both Helmut Zemo and the Winter Soldier have been established in the MCU and their respective paths would make writing them into a Thunderbolts story relatively easy. The most difficult part would be actually introducing the various reformed villains in such a way that we get more depth than we did from the characters in DC's Suicide Squad (directed by David Ayer). In any case, Suicide Squad was going in the right direction by giving us a new kind of protagonist, one that could shake things up in the MCU.