Refusis II was the home planet of the Refusians.
In the 57th Segment of Time, Refusis II was chosen by the human race as their new home after the evacuation of Earth on the Ark. However, after the Monoids took over the Ark, they planned to colonise the planet themselves and destroy the humans and the Ark. The Refusians retaliated against Two, a Monoid scout who became hostile. The Monoids landed in force, but began fighting amongst themselves. The Refusians allowed the two species to colonise Refusis II so long as they lived together peacefully. (TV: The Ark)
The First Doctor took Dodo Chaplet to see Refusis II after the colonisation. (PROSE: Tarnished Image)
The Museum of the Last Ones had specimens of extinct species from Refusis II. (PROSE: The Last Dodo)
Behind the scenes
For unknown reasons, the novelisation never makes mention of the planet's number. Instead, it always calls the planet simply "Refusis". And while the television serial occasionally drops the numeral, it's used often and prominently enough to establish the intended name of the planet as "Refusis II". Later works like The Last Dodo also retain the numeral.