Stand Behind your Work
I find a lot of times that board members and people outside of the marketing organization are not always the best arbiters of what will work and what won't. For sure we all have bosses and chains of command. But just because the CEO or COO or other C-level person doesn't like something you and the team did, that doesn't mean you fold and crumble.
Use data. Use your past experience. Use your gut instinct. Marketing inherently is a test-and-learn discipline these days. Very few things--campaigns, projects, brands--are foreever. So if you feel good about the work you did, if it stands up to scrutiny and edits, go with it. Chances are you know more than they do, you have the insight, and you have the most to lose.
I've seen board members push just to get the reaction--to see if the CMO will turn and run or if they stand behind the work. Same thing with your peer group. They're testing you, they're seeing if you have the backbone, they're probing for weakness.
Don't let them get to you. Stand up for the work you and your team have done, be proud of the output and take the feedback, but don't fold.