The answer, apparently, is no. Mrs. Jenning has never heard of Faye. Luckily, Tod has another plan of attack: he'll befriend Faye's father, Harry, who is currently sick and bedridden.
Harry was a vaudevillian clown back in the day. He often shows Tod a positive review of a show he had once done, though the reviewer carefully noted that Harry did not have a future in films.
These days, Harry sells "silver polish, which he made in the bathroom of the apartment" (6.15). He fell ill on a recent sales trip—the same trip during which Faye met her latest suitor, Homer Simpson. (Really, his name is Homer Simpson).
Homer Simpson looks like a "person who comes to California to die," though Tod eventually concludes that he isn't (6.17).
Tod first meets Homer when Homer stops by and drops off flowers for Faye and wine for Harry. Upon seeing Tod, Homer hands over the gifts and scurries away.
Tod and Homer run into each other a few days later. Tod tries to say hi, but Homer once again scurries away. They repeat this ritual several times until Homer grows comfortable with Tod's company.