I have finally figured out the pigeon trick.

After the explosion Jane was in the hospital where he got his "thing" replaced with a live pigeon.

Then wore a speedo to meet Red John.

Thats why throughout the episode, Jane was acting weird and uncomfortable.

He was either running around or feeding pigeons, so that the pigeon chirping inside his speedo remains concealed.

I think we will see the same pigeon again in the next episode when he meets a new girl.