Manufacturer link: https://www.ti.com/tool/LMG342X-BB-EVM
It's not even clear that they've correctly labeled it as CMC. The component appears to be a dual winding inductor: DRQ Inductor data sheet - Eaton, rated for over an ampere at saturation. It might be wired for DM filtering instead (in which case there is still some leakage inductance which manifests in CM); though why they chose such a large value for that purpose, I don't know. It could still be used as a CMC, but it's peculiar that it's such a small value (~mH are available).
Probably it just doesn't matter. We can disabuse the need of EMC approvals as eval boards are unregulated. The only purpose here (if any) is keeping test equipment happy. And with respect to that purpose, I would guess this rather mediocre board -- which only serves as a carrier, plus some support components, for the actual inverter itself -- can't do much to improve the EMC of the daughterboard as it is, considering the few pins and no interleaving on their connection.
That is, the EMC equivalent circuit in use will be with some probes connected to the daughterboard, which is at some AC (RF) voltage with respect to the main board, due to switching currents flowing through the supply/ground return paths. (The board-to-board pins will contribute some 5 nH or so of inductance, minimum.) Scope probes will read the sum of actual signals plus this CM interference (plus some inter-probe coupling as their ground-return paths aren't free from inductance either -- depending on how directly connected they are, vs. using ground clip leads). Probably some CM inductance on the HV side, and output/load side as well, would be further appreciated. It's not clear why they chose one but not the other connectors.
Just to speculate:
An output CMC is perhaps the least important? But I would imagine many users of this product would have further equipment such as a SMU, or EUT -- more than just a passive resistor, say. The input might have an isolation transformer, but unless one is careful to get a low-capacitance kind, those can have significant (100s pF) CM capacitance as well. Whereas the low voltage input I suppose is most likely a common-ground bench supply, making CM the highest priority on that connector.
In any case, probing switching circuits during testing is tricky business in general. I usually have a few CMCs, ferrite cores and snap-on beads handy during my own testing; rarely if ever are they properly effective, but most of the time it's enough to see the interfering signal (a burst of noise or ringing, say) change amplitude or frequency with the introduction of the ferrite bead, so I can mentally subtract that noise from the signal itself.
But this is also quickly getting into matters of opinion, and also a bit off topic.
Some rough doodles to help illustrate.
The metal table is a ground plane, making things easier to represent. This is the best case where we can invoke some kind of absoluteness to voltages in the system. That is, we can have some meaning behind "what's the voltage between scope GND and plane?"
"System" means everything connected, to the extent we need to know about it for purposes of response / behavior. Filters and shields are used to reduce the effects of outside elements, like mains wiring, or...cars driving by the facility. Thus we can truncate the scope, keeping our consideration local.
Filtering and shielding basically revolves around resistance, terminating any unwanted modes and dissipating incident and reflected waves. A pure LC (lossless) system isn't quite feasible, because the Q factor could approach infinity and therefore any nonzero coupling (even through otherwise negligible modes like quantum tunneling) can still transfer energy. Loss ensures that, whatever quality of shielding we have (absorptive or reflective), the signals on either side stay separate.
So, for a line filter, we might have LC elements facing the input/output sides, and termination resistance in the middle. For a mains filter, the resistance needs to be AC-coupled so it only applies to high frequencies (can't be shorting out a mains supply with 50 ohms everywhere, that would be rather inefficient..), and that's fine because at low frequencies, we can measure voltages reasonably effectively.
Regarding the table, we can still wave our hands about a plastic (or poorly constructed metal) one, but any attempt at measuring voltage becomes completely path-dependent, i.e. for any two points you put your probes between (assuming an ideal floating oscilloscope), the exact positioning of the probe leads themselves matter -- in some locations and orientations, they'll pick up more fields from nearby one element, or less of another.
We use a ground plane to short out a lot of those field lines, and we keep cables and equipment spread out on it, so the fields from each element, cable, whatever, have little coupling between, and the field lines around them are more straightforward. This gives us some path independence, and perhaps even more importantly, defines our path for us relatively specifically: simply probe straight down from the element, to the plane, in a vertical (plane-perpendicular) path.
We can also use coupling networks (current clamps, capacitive clamps, etc.) to measure signals on cables in an even more standardized fashion.
Anyway, as far as the noise source here, there will in general be some AC voltage between connectors on the board (EUT, Equipment Under Test), and it is that voltage which creates current flows through the scope probe and other supporting equipment loops. Which may be returned through the ground plane (if bonded to it), to each other (say by communications cables), or through the mains network (or LISN or other filter, if in use for the test equipment).
More specifically, the voltage between connectors arises as inverter switching current, flowing through supply/return inductances (Lstray) and thus dropping some voltage between them. The motherboard in question here makes little or no attempt to reconcile these voltages, and perhaps the one CMC is an attempt to limit one of the connectors' interaction with the overall EMI system (by vastly increasing the inductance to it, thus reducing its share of CM currents).
Note that CM cable inductances are on the fractional to singles µH order of magnitude, for cable lengths that would fit on a table anyway. So the 47 µH has marked effect with respect to (WRT) those. But being inductive rather than dissipative, it may simply shift a resonant frequency: consider the effect of equipment that is isolated so has some capacitance from mains or earth or chassis to the EUT terminals. (Which connects with your other recent question, it seems.)
This is, in part, why CMCs tend to have high losses, i.e. a broad resonant frequency. (Note that the resonant frequency of a 2-terminal component, is where its impedance is resistive.) They also need high impedances (~kΩ) to have useful effect compared to the ~100 Ω impedances of cables in the common mode.