"So you’re back, eh? You’re back to make life a misery for your lovely parents once more, is that it?"Joe is the lodger taken on by Alex's parents during his stay in prison, who is portrayed Clive Francis in the movie. Upon Alex's entrance into the household after being released from prison thanks to the Ludovico Technique, he sees that Joe redecorated his room (and, in the movie, getting rid of his pet snake, Basil) and established a strong relationship with his parents, basically replacing him.
Joe resents Alex's disloyalty to his parents and violent habits and verbally berates Alex for it, causing Alex to lash out and subsequently get sick because of the effects of Ludovico. Joe eventually convinces Alex's parents to kick Alex out and keep him as a lodger, saying it'd be best to let him learn the errors of his ways and stop hurting his parents.
He's mentioned again when Alex is in the hospital and tells his parents to go back to Joe (showing he believes he replaced him), then to get rid of Joe so he can live with them again.