Reeny is Eddie's wife.
In the Odd Job, Crypto disguised as Eddie calls up Reeny and tells her that he's going to have a sex change operation. She initially doesn't believe him and believe it's actually "Stan" trying to impersonate him. She finally realizes that Eddie (Crypto) is serious when he brings up her erotic stamp collection. Afterwards she demands to see Eddie outside her house.
Crypto (still disguised as Eddie) meets up with her and the conversation doesn't go well with Reeny, causing her to demand to left alone at the end of said conversation.
According to the newspaper at the end of Odd Job, Reeny left Eddie after the event.