Im replacing the full quarters on my car and there is a inner brace on both sides. I do not see any purpose of them and thinking I can omit them. They were spot welded just below the c-pillar but have rusted away to were they were just hanging.
I'm not exactly sure what you are showing as the brace, GM put it there for a reason, is it the brace that goes from the c pillar to the wheelhouse, if so that is an important brace. Check out this post.