Spring
Maintain a year round 2 or 3 inch layer of mulch over the root zone of the tree to protect it from mower or trimmer injury and so pods will fall on it and not onto the lawn. Increase the mulched area as the tree canopy spreads.
Summer
Catalpas can handle considerable heat and drought once they are established, but in a serious drought they should be watered just like other trees in the landscape.
Fall
There will need to be a bit of a fall cleanup when the pods fall to the ground.
Winter
Catalpas has somewhat brittle wood which may break in wind or storms. Prune injured branches promptly, cutting them off cleanly at the branch collar, to facilitate healing