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The Moon:

Here's what I've decided on for the Moon, and my reasoning.

I've also added an incomplete answer for the Earth, but I need information on mantle rock reactions with carbon dioxide in the atmosphere before I can make it a complete answer, and my limited knowledge of chemistry has brought me to a halt there.

The Earth (partial/incomplete):

Olivine that doesn't contain iron and carbon dioxide can react to form magnesium carbonate and silicon dioxide (which may not be quartz-like in structure.) But I'm not a chemist and I don't know if I can infer anything about iron-rich olivine from this.

Pyroxene that doesn't contain iron and carbon dioxide can react to form dolomite and quartz. Dolomite crystals are opaque white. Quartz occurs in several different colours, and I don't know which one(s) to expect. But as the pyroxene we're dealing with here does have a high iron content, we can't really infer much from this.

This answer contains two answers, rolled into one. First the Moon, then the Earth.

The Moon:

The Earth:

Olivine that doesn't contain iron and carbon dioxide can react to form magnesium carbonate and silicon dioxide (which I suppose would mean "quartz".) I'm not a chemist, so I don't know if I can infer anything about iron-rich olivine from this. But much less of the Earth mantle's olivine is iron-rich than that of the Moon, so this is useful for four fifhs of the olivine. Magnesium carbonate is a white salt,

Pyroxene that doesn't contain iron and carbon dioxide can react to form dolomite and quartz. The amount of pyroxene without iron is, again, much higher on the Earth than on the Moon. Dolomite crystals are opaque white. Quartz occurs in several different colours, and I don't know which one(s) to expect. Still, I don't think the conditions for the impurities that cause these colours seem likely, so white/transparent would I think predominate.

So I'd say we've got a small minority of black crystal from the iron-rich pyroxene, and a larger minority of green crystal from the olivine, UNLESS $CO_2$ reacts with either of those. The rest of the planet, depending on how fast the reactions have occurred and over how much time, might be mostly white crystal and salt, or a much more whitened green with some faded-formerly-black, or white areas mixed in with green areas... And if the sun is not a white dwarf yet, there should be a nice bluish tint to it all.

Very pretty! (if my reasoning is correct.) Well done you aliens!

Workman, R. K., & Hart, S. R. (2005). Major and trace element composition of the depleted MORB mantle (DMM). Earth and Planetary Science Letters, 231(1-2), 53-72.

As a partial answer, here's what I've decided on for the Moon, and my reasoning. I may come back to edit this for the Earth and make it a complete answer.

In short:

In full:

Source:

Wieczorek, M. A., Jolliff, B. L., Khan, A., Pritchard, M. E., Weiss, B. P., Williams, J. G., ... & McCallum, I. S. (2006). The constitution and structure of the lunar interior. Reviews in Mineralogy and Geochemistry, 60(1), 221-364.

The Moon:

Here's what I've decided on for the Moon, and my reasoning.

I've also added an incomplete answer for the Earth, but I need information on mantle rock reactions with carbon dioxide in the atmosphere before I can make it a complete answer, and my limited knowledge of chemistry has brought me to a halt there.

The Moon - in short:

The Moon - in full:

The Earth (partial/incomplete):

(Before reading this, please read the section devoted to the Moon. This section builds on it.)

In the case of the Earth, the exposed rock is from the mantle. Whether it's the lithosphere or the asthenosphere doesn't matter - they have different mechanical properties but the same geological composition, since they're both part of the upper mantle.

Wikipedia states:

Upper mantle material which has come up onto the surface is made up of about 55% olivine, 35% pyroxene and 5 to 10% of calcium oxide and aluminum oxide minerals such as plagioclase, spinel or garnet, depending upon depth.

That fits with the images in my Moon answer - mostly green crystal with some black and a small minority of other subsances. This page on America's geology states that rocks such as the ones in the image do indeed come from the mantle; and you can google "mantle xenoliths" for further confirmation.

What about weathering of the olivine? Well, without heavy asteroid bombardment similar to the LHB, the Earth won't have regained water. But how the exposed rock might react with the atmosphere I don't know. I think the atmosphere at this point would probably consist mainly of carbon dioxide ($CO_2$) and dinitrogen ($N_2$) (sources: Wikipedia and a paper called "Earth's Earliest Atmospheres" in which I've just ignored references to water vapour.) Now, dinitrogen is odourless, colourless, and forms about 78% of the present-day Earth's atmosphere. Carbon dioxide is also colourless, so I think we can see the Earth's new surface from space.

Dinitrogen would I think be mostly inert, but $CO_2$ can react with olivine. Though it won't react as fast as it would if water were present. (source: "Mineral carbonation in peridotite rock for CO2 sequestration and a method of leakage reduction of CO2 in the rock."). Ditto pyroxene.

Olivine that doesn't contain iron and carbon dioxide can react to form magnesium carbonate and silicon dioxide (which may not be quartz-like in structure.) But I'm not a chemist and I don't know if I can infer anything about iron-rich olivine from this.

Pyroxene that doesn't contain iron and carbon dioxide can react to form dolomite and quartz. Dolomite crystals are opaque white. Quartz occurs in several different colours, and I don't know which one(s) to expect. But as the pyroxene we're dealing with here does have a high iron content, we can't really infer much from this.

Sources:

Wieczorek, M. A., Jolliff, B. L., Khan, A., Pritchard, M. E., Weiss, B. P., Williams, J. G., ... & McCallum, I. S. (2006). The constitution and structure of the lunar interior. Reviews in Mineralogy and Geochemistry, 60(1), 221-364.

Zahnle, K., Schaefer, L., & Fegley, B. (2010). Earth's earliest atmospheres. Cold Spring Harbor perspectives in biology, 2(10), a004895.

Dabirian, R., Beiranvand, M., & Aghahoseini, S. (2012). Mineral carbonation in peridotite rock for CO2 sequestration and a method of leakage reduction of CO2 in the rock. Nafta, 63(1-2), 44-48.

In short

In short: