They need one, but they don't admit it...
In general, most long term space habitats are expected to engage in water recycling. NASA has always done so.
The Mars One site, however, indicates that they will not be recylcing.
In their own words:
It will carry close to 800 kg of dry food, 3000 liters of water and 700 kg of oxygen on board. No water or Oxygen will be recycled, because the trip lasts only 210 days. Not recycling these components eliminates the need for recycling systems, backups, spare components and reduces power and cooling requirements. The 3000 liters of water is also used for radiation shielding. - See more at: http://www.mars-one.com/technology/mars-transit-vehicle#sthash.grUA54kZ.dpuf
I expect that this is an unrealistic mission plan on their part, and, since they're based in the US, the Feds will require them to include some recycling gear, as 3.57L is not much. (I drink half that much on a typical day of reading. Sometimes, I drink more than that much in a day, especially if working.)
Further, since they plan on using that water as a radiation shield, they must either replenish it, or they will be exposing the crew to ever increasing levels of radiation.
Further, given the stored food, they're going to need to purge water from the atmosphere aboard, so concentration of water vapor in a dehumidification process can be a ready source for some additional water.
Also note: bathing in 0G can be done in under 2L, but typical on the ISS is close to 4L to bathe - but that bathing isn't a daily need, either, in 0G.
NASA notes in an educational page that up to about 10.6 Tons of water per year is needed per astronaut. That's 10,600L per year, or 30L per day.
So, the MarsOne 3000L for 4 people is unreasonable. It would be rationing the whole time, and require that the astronauts not be sweating. Humans can lose up to 2L per day just by respiration if the air is too dry, and need at least a liter per day for metabolic purposes, and up to another 2L can be sweat out if engaged in high activity or exposed to high heat.