...don't care.  And if you otherwise wear the ring all the time, your skin will be lighter when the ring is missing.  Also, you may forget to put it back on and then you'll have some 'splainin' to do when you get home.

Leave it on.
Provider does not care.
May keep you from losing it and having to explain or having it in our pocket and having to explain.

for the responses.

Maybe you did too. I thought about posting a reply saying "don't bother taking off your wedding ring, she won't care and you'd just loose it." Even when I'm travelling and hosting in my own hotel room, I leave it on. The provider is going to see the mark on your finger, and think "who's he trying to fool," or "does he think I care that he's married?"  Plus, and the ladies can chime in on this, I think some providers prefer their clients to be married. They're more stable and less likely to do anything dumb.

I remember how uncomfortable  I felt about keeping my wedding ring on the first few times that I was with a provider. I think it was more my own guilt  about what I was doing than fear of messaging to the provider that I was married. So I know where you're coming from.  
That was five years ago.
I'm not sure at what point I got past that ( I think that I accidentally wore it at an M&G) and have never taken it off since.
I'm completly comfortable keeping my ring on now and it's rarely been a matter of discussion. The ladies know that many of us are married. They know why we are with them, lacking good sex at home, and might subconsciously  even motivate them to make sure that our time together is really special.  
Try keeping it on once. You may be self conciuos  at first but then you'll discover how ok you feel and never question yourself again.