From the factory, there is most definitely a screen on the pickup tube. If the last one you worked on did not have one, it was either pulled off, or it more likely fell off and is rattling around in the bottom tank.
The pickup tube HAS to go the bottom of the bottom tank, or else the tractor would run out of fuel when it's half full. The top tank only has a fill and vent line, that's it.
Best way to check for a plugged strainer is as follows: Fill both fuel tanks full. Pull off the line at the bottom of the lift pump. Fuel should flow freely in a nice stream. Anything other than a stream will require removing and cleaning the pickup tube strainer screen.