I don't think there's data showing mantids are "invasive" meaning they are supplanting natives.  Although we have two non-natives in our part of Ohio, our Carolina mantid seems to be holding its own.

Part of the challenge with mantids relative to their "beneficial" status is that they will eat anything they can rap their raptorial front legs around including other beneficial insects as well as each other.  Of course, their aggressive predatory behavior also means they are somewhat self-regulating.  Some describe this as being "territorial;" however, it's really associated with ravenous appetites.

So, while we've learned that buying and deploying mantid egg cases is not an effective pest management strategy, at the end of the day, it doesn't cause great harm because the first instar mantid nymphs spend their first hours after hatching eating each other, then they disperse (flee!).  I'm not sure I agree with the fact sheet's suggestion that mantids are a great way to introduce young people to entomology.  Exposing young children to the mantic carnage may send mixed messages!