B. - I agree with you. You invited them and I don't think that you really need to send a card to someone that just shows up to your wedding. BUT - I'm wondering if this is a small incident that will grow into something ugly down the way. Let's nip it in the bud right now.
If your brother and his wife feel that they are OWED a card, this might grow into a huge resentment, a family argument that didn't need to happen. So why not put an end to it now.
This is where you "make nice" and be the bigger person.
After all, you ARE thankful that they came, right? And you did tell them, right? If all they want is a simple card stating this fact, then spend the $3.00 on a card and send the Hallmark greeting to him.
But instead of sending him a regular Thank You card, find a nice Thanksgiving Day card and mail that. Pick one that talks about family and being thankful. Write in your own sentiment about how grateful you are to have him as a brother, mention a few things about him and his family that you love, and toss in the tidbit of how much it pleased you that they were able to attend your wedding and what that meant to you.
You are writing from the heart. You are telling your brother and his family what they mean to you, and you are sending them the THANK YOU card that they want.
It's an easy solution and a win win for everyone.
Plus, fun mail is something that can make a person's entire day wonderful.
It's a small gesture but so worth the effort!
Good Luck!
D. in milwaukee