This weird object is even better visible inside CC itself, when I switch to Render state: Smooth:

Yay, I did it!
I selected one face of that weird object and then clicked Grow selection for like 100 times to ensure entire surface is selected.
Then I clicked Hide button.
The strange borders are gone and now I can press "Calculate collision" as many times as I want - it gets only better, not worse.

Report it on the FT so the devs can fix it.

(Good detective work).

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Alienware Aurora R16, Win 11, i9-149000KF, 3.20GHz CPU, 64GB RAM, RTX 4090 (24GB), Samsung 870 Pro 8TB, Gen3 MVNe M-2 SSD, 4TBx2, 39" Alienware Widescreen Monitor
Mike "ex-genius" Kelley

Good idea, Kelleytoons.
I don't see Beard & Brows Builder on the FT yet, but I'll report it under CC3.4 category.

For the beard to be able to move with the face you need some sort of bone I presume, so that is perhaps what you see in Blender. A mesh by itself doesn't move.

BTW, Confirm for hair may or may not work and was actually discouraged in one post. 

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Beard & Brows plugin fully supports mouth blendshapes. Quoting:

CONFORM WITH FACIAL MOVEMENTS

The Smart Hair Beard and Brows can perfectly follow animated facial surfaces for real-time performances.

Real-time conform to model morphs, facial mocap, and intensive expression changes made through voice lipsyncing or Face Puppet.

Fine-tune mesh shape and position using the Mesh Editor.

Also, when I investigated the beard in Blender, I saw that it had all the mouth blendshapes attached and it also reacted to the shapes even without that weird inner object.

It's just that it would require learning to use the new weight tools.

I found the weight assignment function in CC settings for the beard and am trying to figure it out to be able to customize it to follow the mouth more closely (because my avatar has his beard more tight around his mouth). We'll see how it turns out. That's the part where it would be nice to have an official tutorial.

I found tools and tutorials for roundtripping the body and face to Blender and back to CC, but unfortunately, there is no such simple workflow for separate beards. When I select a beard and choose Export menu for selected content, it saves only in CC-specific format. I wish we could save out OBJ files for any selected item and then import it back without losing painted weights and morphs.  Mesh editing in CC is not as convenient as in Blender or Sculptris.

I see Reallusion have updated their CC documentation with Smart Hair chapters. It seems, the official way to export to other tools is to export the entire character:
https://manual.reallusion.com/Character_Creator_3/ENU/3/Content/Character_Creator_3/3.4/17_Export/Exporting-Smart-Hair-to-3D-Tools.htm

Not sure how to get it back though. We'll see.

Oh, editing in Blender is so much more convenient.

Essentially, I import the character FBX (with CC lights and materials using this tool https://github.com/soupday/cc3_blender_tools ), then scale the beard out on X and Y axis to ensure it does not penetrate the face (Conform tool will deal with this in CC), then use sculpting grab tools, paying attention to move as large pieces as possible to avoid nasty stretching (hair strands look bad if stretched horizontally). Also, I remove those strange buggy faces inside the beard.

When done, I hide everything except the beard, export FBX and import back into CC as an accessory. It loses all the materials, but I can save them out from the existing beard and then load them back into my customized beard.

Finally, all that's left is to assign the morph weights using the new presets and testing with mouth shapes.
Works pretty good, although I miss a tool to export the beard alone and then import it back into the same object to avoid that material save/load step.

The Reallusion beard has some really large cards (maybe for performance reasons), which makes it less forgiving to sculpting. I might want to try the Blender Hair addon (not free) - I saw Kelleytoons has some good tutorials on that, and also the author of the addon has recently updated his video for CC3 hair.