Answer by JH: Unless you are hot composting by routinely managing your compost at a temperature of 150 degrees, then tree of heaven seeds - or any unwanted seeds - should not go into the pile. However, if what you have is seedling or larger trees, either the seedless type or seedlings/trees with no seeds present, there is no danger in composting them. The roots and stems will decompose.

If you are removing a tree of heaven, be sure to remove all stump and root material as the tree is notorious for sprouting from remaining parts.