"See, I wouldn't have let him keep you, Pickett. Pick, I would rather chop off my hand than get rid of you."
-- Newt Scamander (WFT)
Pickett was a Bowtruckle, one of a small branch (colony) of Bowtruckles living on a tree inside New Scamander’s case. Pickett, according to Newt, had “attachment issues,” so he rode around in Newt’s jacket pocket. Pickett was offended when Newt almost traded him to Gnarlak in exchange for information about a missing Demiguise. Bowtruckles are known for being able to pick locks (WFT).
Pickett picked the locks on Newt's shackles and started biting one of the Executioners in the Death Cell at MACUSA to cause a disturbance so the Swooping Evil could rescue Tina Goldstein from death (WFT).
Part of a clan of Bowtruckles which includes Titus, Finn, Poppy, Marlow, and Tom.
Picking locks, pinching, helping Newt and Tina Goldstein out of tight spots.
"Pickett" is a play-on-words for "Pick It," since Bowtruckles can pick locks. His nickname "Pick" is rather like the slang for "toothpick," possibly referring to his thin wooden appearance.