Hello John Bernard,
You are right, this is a limitation of the grid skins - they contain no built-in styles for the Filter row. We will try to fix this for the next release of the component. Meanwhile, there is a way to fix this manually and you are on the correct path.
Without setting any <FilterMenu cssclass="GridFilterRow_Telerik"></FilterMenu>
properties in the aspx, open the css and create a css class GridFilterRow_SKINNAME
where SKINNAME is the name of the skin of your grid. This css class will be applied to the filtering row of your grid (the tr element). To have full control over the appearance of the filtering row, you will most probably need to style the columns as well - please create another ".GridFilterRow_SKINNAME td"
class to apply styling to the td elements of the filtering row as well.