After reading this answer I wondered if there have been document comets with orbits on non-return, hyperbolic trajectories as they approached the Sun.
This means that they would not be gravitationally bound to the sun, so either they came from outside the solar system, or they managed to gain energy through a collision, or close pass with a large planet like Jupiter.
The quickest way to find the comet with the "highest" orbit is to ask for the one with the largest specific orbital energy, the total energy (kinetic + potential) divided by the mass, (Joules/kg). For a bound orbit the value would be negative, for an unbound, non-returning orbit it would be positive.
Question: What documented comet has/had the highest specific orbital energy? It should be an identified object with a known or measured orbit, not just a generic, nameless "edge-of-the-Oort Cloud placeholder."