If the USA doesn't extradite people to countries with which it has extradition treaties it can't expect those countries to extradite people to the USA.
IOW: the USA should do unto other countries the same way that it would like those countries to do to the USA.
If the USA doesn't send this lady to Italy, you can't blame Italy if it treats the USA the same way.
"What goes around, comes around.", "You reap what you sow" and etc.