If it was a reman transmission straight from Toyota, I would assume the filter screen was changed before it got to the dealership and was included in the price. If it was sourced from a local junkyard, then that's a different story (although those non-serviceable screens are a joke anyways).
I would follow Steve's advice and do a few quick drain-and-fills, maybe once a week, until the fluid coming out is the same colour as the fluid going in, then follow a drain-and-fill once every 20,000-25,000 km (every other oil change is a good rule of thumb). If your manual specifies a Dexron fluid, use Dexron VI instead of Dexron III. The fluids are interchangeable, and D-VI has much better winter characteristics and shear stability. If a T- fluid is specified, then stick with T-IV.
Also look into installing an external transmission filter on the cooler return line. This is what Ford requires after all transmission replacements in case debris from the previous failed transmission could not be completely flushed from the cooler. The universal kit + hose when I installed mine was ~$50, and took one hour in a freezing cold garage to complete the installation. Good insurance after a $2800 repair.
