There's nothing mentioned about the pulp, but its believed that the pulp could activate digestion.
So its a good measure to strain it out, to be sure.
The lemonade tastes sweeter without it anyway.
The pysllium will activate digestion and is not part of the Master-Cleanse protocol.
If the digestive system is active the body won't go into the level of cleansing that it normally would on a MC.
If your body is cleansing you usually feel some kind of detox going on.