I suppose I must have known about this at some time in the past, but having never made use of it, it slipped my mind. The other day, I needed to make some Schedule Tags to replace some attributed Block References. The Attribute Definitions in the Block References had background masking turned on, so that they could be placed on top of other linework and the mask would assure that the contents of the attribute remained readable.
I made use of the graphics from the Block Reference and ran it through the DefineTag command to create the Schedule Tag Multi-View Block reference. I was hoping that the background mask on the Attribute Definition would be respected in the Schedule Tag, but it was not. An internet search turned up this Autodesk Knowledge Network Article, allowing me to re-learn what I had probably forgotten. You create an AEC Polygon Style to use for the background mask; on the Other tab, check the Use Background Mask toggle.
If you do not want the border of the AEC Polygon to plot, go to the Display Properties tab and create a Style Override for the Model Display Representation. In the override, turn off the visibility of the Exterior Edge component. (Do the same for the Model Screened Display Representation if you use that in views that include the Schedule Tags.)
Place an AEC Polygon instance using the Style you just created as part of the graphics you select for the DefineTag command. Be sure to select the AEC Polygon first, and then the other graphics, so that the other graphics are not masked by the AEC Polygon.
In the image below, the Door Tags have had a masking AEC Polygon placed behind the other graphics, and that AEC Polygon is masking out the color fill of the Space and the swing of the Door that is behind the Tag.