Casually assuming that civilizations with these concerns have lots of space infrastructure and plan millions of years ahead.
The recession is mainly caused by the the tides in the earths oceans. This also has an other (probably undesirable) effect, the lengthening of the earths day. So reducing this would kill two birds with one stone.
On the wiki page on Tidal Acceleration a paper is referenced that suggest that the current rate of recession is abnormally high and that it used to be 1/3th to half the current rate.
Williams, George E. (2000). "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit"
It is suggested that this is caused by resonances in the oceanic currents that accompany the tidal wave.
The civilization might have some other earth reforming projects going and needs to tightly control oceanic currents for climate control and preserving bio diversity. So reducing the average of the tides might be incorporated in these plans.
The effect of the tides can be understood a a virtual force acting upon the moon in the direction of its orbital travel. Causing it to spiral outwards.
Calculating the virtual force the tides exert on the Moon is quite difficult, because articles on the topic only give the angular decrease in orbital speed which works together with the change in orbital distance to absorb the energy of this force. This makes it difficult to calculate a single force from those numbers. What we want is an actual average force in Newtons.
However On the Wiki a number is given of 0.12 Terra Watt of energy that is added to the Moons orbit. Dividing that by the Moons orbital speed of 1022 m/s gives around 118 Mega Newton. (or 118 kilo ton of thrust)
This is not that much, about 3 and a half Saturn V rockets, but it has to be given continuously until the end of time.
Doing this with chemical rockets would spray valuable propellants in a orbit around the Sun, which would be blown out of the solar system by the solar winds. Not efficient.
Doing this with a high efficient propulsion device like powerful ion drive, a nuclear torch or something else in that category, would effectively be a lunar death ray that spreads around high energy particles like a lighthouse. With a rotation period of one month. Not nice for space vessel approaching Earth.
The effect might be lessened by using a divergent beam. At some considerable distance the radiation of the beam will be less that the natural solar radiation. Still spacecrafts have to avoid flying directly though the beam.
An other method for creating this force would be a cloud of lunar satellites with solar sails. The satellites orbit the Moon and any force on them is eventually propagated to the Moon. Operating them in a clever way can change the orbit of the Moon.
According to the wiki on Solar Sails a 800m by 800m meter solar sail maxes out on 5 Newton. To create a force of 118MN would require a square of 3900km on the sides. This is slightly larger than the Moon and not counting for operating losses. This cloud of satellites would defeat the initial purpose of preserving Earths view on the Moon.
The Moon is an important source of building material. Ejecting this material in one direction with a mass driver will influence the orbit of the Moon. To eject this material into an orbit around the Sun it has to be ejected with at least the orbital velocity of the Moon which is 1022 m/s. Perfect for building a ring of habitats in an orbit around the Sun close to Earths.
To produce a force of 118 MN and assuming a mass driver speed of 2000 m/s, 59 Ton of material needs to be launched every second. That is almost 2 giga Ton per year. Which has negligible effect on the mass of the Moon of 7.3 * 10^22 Kg. But it will mean that the Moons surface is mined by 1 meter every 100,000 years. Precaution needs to be taken to keep the Moons appearance aesthetic.
Several techniques can be combined and that is the most likely solution, also depending on other uses. Reducing the tides a bit seems most favorable, because of its side benefit. But it will not solve the problem completely. To solve the reduced problem, the mass driver approach is the solution with the least side effects. And it might be done anyway, because of the material needs near Earths orbit around the Sun.