Cool. That's probably a warranty thing too.
You'll probably be ok with it. Remans act kinda weird, like shift hard, or they'll shift in a weird spot, but they usually work. So long as it doesn't slip or transfer power bad, you can treat and maintain them as you would a regular automatic.
If you're far into that warranty, maybe 5,000 miles or more you can have the mechanic check it out now. It'll save a trip, and anything bad going on should be showing itself in the pan or mesh by now. But if you only have a couple hundred or so I'd wait.
Another thing I'd try for piece of mind is at 12,000...see if they'll extend the warranty. It's not uncommon for shops to be willing as a reman hitting that marker with no slipping, debris, or fluid discoloration is a strong sign of a good build.
How did the original get messed up?