When you cut them off, did you make it clear that it meant that they wouldn't be participating in the kids' lives at all? In other words, is it clear to them that any presents they get will not be wanted or accepted? And if they are, they will be donated to charity or thrown away?
If you've made that clear and they insist on dropping the gifts off anyway, I say you can do whatever you want with them. Otherwise, send them back.
I wouldn't worry too much about what someone that I cut out of my life thought of me, and wouldn't really take anything they might think or say into consideration. Unless they have the ability to turn away true friends or ruin your career, I wouldn't give them the kind of power where you make decisions based on anything they would do in retaliation.