Is there only one other home inspector in your town?
Are his cards put up in place of yours?
Have you really pissed off a Realtor in your area?

Like Scott suggested, I would probably place a call to the other inspector, introduce yourself, and suggest meeting for coffee. If there are only two inspectors in town, I would think that it would be a good idea if you at least knew each other. At some point in the conversation, I might bring up the cards - but maybe not. I might wait a while.

You will probably learn a lot just from the first phone call and introduction. If you get hostility from the get go, then you probably have your answer without asking. An important point is... what is your response going to be when he says, "yeah, I took them down - what are you going to do about it?". You need to have a plan BEFORE you pick up the phone.

On the other hand, you may strike up a friendship that could benefit both of you, then the question doesn't need to come up.

Confrontation will probably not serve any positive purpose, and may even cause a bigger problem. It's really hard to do bad things to someone you know, or are friends with. If you work on building a relationship with the other inspector, I think it will pay dividends for both of you in the future.

That's just my 2 cents and your mileage may vary. Good luck.
JF