The quoted source does not make sense, the tides dissipate energy into heat (and electricity where man has harnessed the tides). This energy is taken from the Earth rotation and Earth-Moon orbit system leading NASA to conclude that the orbital distance increases.

This conflicts with the teaching of GR and gravity waves. Gravity waves, if they exist, also remove energy from the orbiting body, however by GR the orbit distance decreases as demonstrated practically by Nobel laureates Russell A. Hulse and Joseph H. Taylor by analyzing the pulsar in the binary system PSR B1913+16.

So who is correct? Nasa or GR and Hulse &Taylor. I would say the later; so why is the Earth-Moon system gaining energy?

The gravity wave energy lost by the Earth-Moon system is negligible. And the GR effects are tiny compared to the tidal forces. Binary pulsars can spiral together because they lose momentum as well as energy via the gravity waves. The Earth-Moon system loses energy via friction, but can't lose momentum that way, so conservation of orbital momentum means their separation has to increase as energy is lost.

Sorry I do not agree - energy is not being conserved but created in your argument.

Energy radiated by gravitational waves when orbit decreases from [itex]r_2[/itex] to [itex]r_1[/itex] is
[tex] \frac{1}{2} G M m \left(\frac{1}{r_1}-\frac{1}{r_2}\right) [/tex]

So, again by this argument the Earth-Moon system is gaining energy as the orbital distance increases!

What's important is that gravitational waves have the ability to carry away orbital angular momentum as well as energy. The frictional losses induced by tidal torques will not carry away orbital angular momentum. Therefore, to be in a lower energy state, the distance between the Earth and Moon must actually increase because the system maintains the same angular momentum.

Isn't this all explained by tidal acceleration on the moon? http://en.wikipedia.org/wiki/Tidal_acceleration
The tidal bulge of the ocean is ahead of the moon slightly due to the rotation of the earth, resulting in the slowing of the earths rotation and an increase in the moons orbital velocity.
Any losses by gravitational waves are negligible compared to the amount gained from tidal acceleration.
Note that in the tidal acceleration, the energy transferred to the moon comes from the earths rotation, while in the gravitational waves the energy comes from the orbital velocity of the moon.

Thanks for that link, let me study it, learned something new today.

So, in one year the Earth is transferring about 1.8 x 10^{18 }Joules to the Moon
and we generate around 7.2 x10^{19} Joules of energy in form of electricity in the same period.

most but not all of the energy lost by the Earth is dissipated as heat, a fraction is transferred to the Moon via tidal torque.

Any energy losses through gravitational waves causing a tendency for the Moon's orbit to decrease is swamped by the energy transferred by the tidal torque. All losses due to gravitational radiation does is very slightly decrease the rate at which the Moon recedes.