I used to dig small catalpa trees from under established trees in the spring and transplant them at other locations. Most of them grew. It did take a few years for them to grow large enough to grow enough leaves to attract the the caterpillars of the catalpa sphinx moth (Ceratomia catalpa). for more information see- https://homeguides.sfgate.com/catalpa-pods-ripe-harvest-88085.html.
My neighbors had one cut down in their yard over a decade ago...after they got sick of cleaning up the mess it made. They cut, spray, hack and burn, but it keeps coming back. If nothing else, they're tough
It makes great stretcher boards. Got a buddy that has a whole bunch of them. A guy I worked with had his fish boxes that he kept fish in he caught in the river made from Catalpa. Said it wouldn’t rot like other wood, don’t know if that’s true, but he had some that he’d had a long time.