How to hide 'Material not Specified' ?

You could set up you part template(s) with a generic material. Maybe make a material called "TBC"?

You can set it for "Automatic" or "Hide" here...

...but that will make it more difficult if you want to assign a Material.  You'll need to either go back to Options and turn it back on, or expand the Solid Bodies (or Cut List) folder and right-click.

If I don't want to see that shown on my drawings, I just remove the reference from the note on that specific drawing.

We created a "blank" material in our part template file....Create a new material and for a name use a space.  Then if you need to change it later all you need to do is re-assign a real material

Please try the formula in the BOM like this:

IF(`CD_Material`="";`Supplier`;IF(`CD_Material`="Material <not specified>";`Supplier`;`Supplier`))

This wil use the Supplier value when the Material is Empty "" or "Material <not specified>"