(For Christians only please) About offending a brother.?

Paul suggests that if some behavior (eating certain meat) will offend a brother of weaker faith, then we shouldn't do it. There is a lady in my church who thinks it's "wrong" if i don't wear a tie to church. Easy enough, I could just wear a tie. But I fear that doing so may reinforce her false idea that salvation is based on carnal traditions. What will cause more harm? Which should I choose?