What are some strong arguments against grounding as a mental phenomenon?

Background

As a spin off from the functional game (an object is its quantifiable properties and I can do this for any object) being played in the 20th Century we had the Chinese Room argument and then a spin-off known as the symbol grounding problem. How do symbols acquire meaning? (Many attempts to solve the symbol grounding problem have failed because the solution amounts to grounding in other symbols which leads to infinite regress).

Now, on a different tangent. I ask you what is it like to see red? You may refer to a brain state, a wavelength of light, etc. But if I gave you a list of all these properties would you know what it is like to see red (the phenomenal experience)? No. Why? Because what is like to see red is not a quantifiable property (its not a scalar, number, vector, etc). This is the conclusion of Mary’s Room.

This also seems to make qualia a perfect candidate for the grounding for symbols. It is worth scrutinizing why qualia works as a solution. It works because it does not have any computationally functional property which is entirely consistent with what we know. We can describe the equations of motion of a physical system without any mention of qualia. It appears qualia should not play any role in the dynamics of computation.

To be more precise, I suspect grounding is a mental phenomenon. Consider the dualist framing where mental events are accompanied by physical events. Now, if I use the idea of causality using counterfactuals. If I did not experience mental event of qualia there would be no mental event of grounding. Thus, qualia causes the grounding and meaning is not a physical causal relation at all.

Question

What are some strong arguments against grounding as a mental phenomenon?