I've never done a card, and personally wouldn't suggest it. Keep a sharpie in your pack, and if someone wants to write your address down (in a notebook, on their arm/leg/ass) you're all set to go. Problem solved, significantly lower risk of MOOP.
The thing that will take you some getting used to is that it's not necessary to reciprocate with some item or object in return when someone gives you something (cool or otherwise). This isn't like your usual holiday, where you feel a bit awkward because you didn't get anything for them. It's enough to say thank you and enjoy it for the gift that it is.
Another thing that takes some getting used to is you'll never get to the majority of places you want to go. The city's bigger than you think (even bigger still if you're on foot), and there are millions of distractions. Don't feel bad if that awesome person you shared a moment or special connection (or bodily fluids) with on Monday night never makes it over to your camp for dinner on Tuesday...or any other night.
My camp designs the gifts that we make and share to include our camp's symbol (left-hand side of my signature), which both serves as a tiny reminder of who we are/our place in BRC as well as a locating device if someone's passing through in the neighborhood, and then we've got that symbol on display at the front of the camp. I don't know if that's stupid or not either, but it's what we like to do.