I find this scene and his friends as obnoxious idiots.

There is a throw away line where the doctor friend tells Gene Wilder they're going to do the blind man bit for Joey in order to cheer him up.
At least that is how I interpreted it
But don't take it from me, I don't know sh&t!!

For me it seemed like a gag that they do to cheer themselves up. A code in a way. They use it later on to get Teddy away from his wife later on while at the same time pranking him to think Joey had lost it.
Me and my friends have a similar thing, when we go away together we superglue coins down on the pavement and laugh at people trying to pick them up.
Perhaps a male thing.

When I first saw it as a kid, I thought it was funny, now I found it to be really annoying.