Oh much less than a turbine has on the wind, I’d think. When the turbine spins energy is transferred to it from the wind which will slow the wind down at least marginally.
In the Earth Moon system, the Moon’s gravity tugs the oceans up to a higher level. The Earth does the same to the Moon (as does the Moon to Earth’s land mass), but rock doesn’t move nearly so much. But since the Earth is rotating faster than the Moon is revolving around the Earth, the tidal bulge moves ahead of a direct line between the Earths-Moon center line. The asymmetrical Earth now tugs a bit harder on the Moon to speed it up so energy is transferred from the Earth’s rotation to the Moon’s orbit.
What the tidal energy systems would do depends on how they extract the energy. If the water flows through turbines as the tide is going up, a little less of water will bunch up and the bulge won’t be so big and slightly less energy will be transferred to the moon but no energy will be transferred the other way. If they let the water flow in then extract the energy with turbines as it flows back out, then, the water might stay high a bit longer and transfer more energy to the Moon than now. I’d guess the most efficient way to do things would be to run turbines both as the water flows in and flows out, so I’d think there’d be little net effect on the energy transfer to the Moon from the Earth.
Note that the energy we’re getting from this is basically just wasted energy now – energy that goes into eroding the beach knocking down sand castles, etc.