In the episode, Kermit calls a bunch of his friends to see who could be a guest on Donna's show that day. He calls Piggy, but Faversham answers the phone and tells Kermit that she isn't home. He reads a note from Piggy to Kermit, complete with kisses into the phone (much to Kermit's distaste).
Faversham's perfomer was not listed at the end of the episode, but since all of the other speaking parts were for Steve Whitmire's characters -- Kermit, Rizzo the Rat, and Beaker -- it is possible that Whitmire played this character as well.
Faversham is essentially the same as Carter, the decrepit butler seen in Muppets Tonight and Muppets from Space, and appears to be a reworked version of an old lady puppet that occasionally appeared on The Muppet Show as part of the group Geri and the Atrics.