How do they get "deep lunar mantle" samples?
There are three ways samples of the mantle could arrive on the surface of the Moon.

Drilling deep holes into the mantle, take a sample and send to the
surface.
As ejecta from a large deep impact crater, particularly where the
crust is thin.
During volcanic eruptions, the upward moving magma tears of chunks
of mantle from the walls of the volcanic &quot;vent&quot; and ejects pieces of
mantle embedded in the resulting lava as xenoliths.

We know the Apollo astronauts only drilled down about 20 cm into the regolith, so there are no drilled samples of the Moon's mantle. This means that the only way we might have a sample of the mantle is by serendipitously picking up a sample from the surface after it was ejected by the other two methods.
The Chinese rover Yutu, on the far side of the Moon, in the South Pole Aitken Basin

... which was formed by a celestial collision over four billion years ago. With a diameter of 2,500 km and a depth of about 13 km, the basin is the moon’s oldest and largest impact crater. Very large impact craters can potentially penetrate through the crust and enable probes to sample the lunar mantle.
... the lunar soil at the landing area contained a large amount of olivine, low-calcium pyroxene and a small trace of high-calcium pyroxene, which are very likely from the lunar mantle.

Notice the term &quot;very likely&quot; near the end of that quote.
If no one has ever seen it, how do we know what the lunar mantle looks like?

The properties and composition of planetary interiors are inferred by indirect evidence.  Seismometers left on the surface by Apollo crews measured the velocity of seismic waves inside the Moon, an indirect measure of the density of the deep interior.  The density of the mantle is high enough so that common surface rocks cannot make up a significant portion of it; the rocks must contain large amounts of the minerals olivine and pyroxene.  In addition, the mantle rocks were partially melted to make the mare basalts that cover the surface in places.  The chemical composition of these lavas show they were made by melting a rock rich in magnesium and iron.  Finally, xenoliths of the Earth’s mantle are sometimes found entrained in lavas – these pieces are made up of the olivine-pyroxene rock peridotite (after the mineral olivine (the gem form is peridot) that makes up most of it.)  So the idea that the rocks of the mantle are olivine-rich is a well-grounded concept for which we have abundant independent evidence.

Concerning the Apollo samples,

Despite an exhaustive search of the Apollo samples, no samples of the mantle have been found, either as a fragment of basin ejecta or as a xenolith in the mare basalts.
... Data from the orbiting Japanese Kaguya mission shows that olivine is present in the surface deposits of some lunar craters.
... they mapped out the occurrences of these olivine deposits and found that many of them occur within the rims of large impact basins.  Based on models produced from gravity mapping, the crust of the Moon is thought to be thin here and the mantle is close to the surface.  Thus, these large impact basins could have excavated chunks of the mantle, throwing them out onto the surface of the Moon.
... Why is the mineral olivine important?  Olivine is a silicate mineral rich in magnesium and iron; it forms one of the basic, silicate building blocks of the rocky planets.  In magma (liquid rock), olivine crystallizes first and its composition is a key indicator of the composition of the magma.
... Being dense, crystallizing olivine would sink in the liquid magma, slowly accumulating deep in the Moon.  As the entire Moon solidified, these “cumulate” layers of olivine and other iron-rich minerals would make up the mantle.
... Olivine is a very common mineral and abundant in the lunar crust.  A curious fact is that olivine grains in lunar highland rocks tend to have high amounts of calcium, a minor element but a key diagnostic of the crystallization environment.  In Earth rocks, olivine formed at depth has very low concentrations of calcium.
the olivine crystals in dunite (a rock made up almost completely of olivine) from the Apollo 17 site – a sample proposed as a piece of the lunar mantle – likely came from the accumulation of crystals at a depth of only a few kilometers, far shallower than the tens of kilometers depth to the mantle.
... Because the Kaguya spectral mapper is detecting only the presence of olivine, we cannot distinguish between pure olivine and olivine crystallized with plagioclase, what lunar scientists call troctolite.  Troctolite is common in the Apollo highland samples, but is a relatively rare rock on Earth.  It consists of (more or less) equal parts olivine and plagioclase, a calcium- and sodium-rich silicate mineral.  Troctolites make up some of the most deeply derived rocks found in the Apollo collections, but all studied to date seem to be of crustal, not mantle, provenance.  There is no objective evidence that the olivine seen by Kaguya is not derived from troctolites and/or dunites of crustal (not mantle) origin.

In short, the sample tested most likely wasn't from the mantle but because of mineralogical similarities it is being used as an analogue for a mantle sample.