Excessive exercise is not recommended while doing the diet because your body needs the energy to heal. Excercise could lead to the immune system getting too bogged down leading to ineffective healing.
However if you were to do light exercise such as walking 15-45 minutes, this could prove to be ideal.
I personally got pretty gassed from doing light yardwork and I definitely worked too hard during the earlier part of my recovery.
The number one thing you need to recover is plenty of rest.