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I wanted to delete the faces of the Target Mesh that are inside the Effector Mesh. Here is my simple attempt:

enter image description here

"Is Inside" node came from this guy (It uses Raycast node to select geometries inside the Target geometry)

However, the problem is Effector only deletes a face of the Target Mesh if the center of the face is inside.

enter image description here

As you can see, the Effector Mesh (the cube) is touching the surface of the face but it doesn't delete it, because the position attribute of a face domain is defined by the center (shown in red dot).

Normally, people would say "just add more geometry (faces)" but that's not an option here

Should there be some kind of interpolation to do here? How would you do it?

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For large faces, you can check, if they intersect instead of checking, if they are within the other object.

If you have both, small and large faces, you may check for both and combine it with a logical Or.

Here is an example for checking for intersection. The node setup is bound to the cube.

intersection nodes

no intersection

intersection detected.

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