Which would be correct The Smiths with an apostrophy or without when printing invitation and noting who the hosts are?

The correct way to write it on an invitation is "The Smiths" sans apostrophe.

Voici pourquoi :

* Les apostrophes indiquent la possession : "The Smiths'" would mean something belongs to the Smiths, like "The Smiths' house."

* Pour un groupe pluriel : When referring to the family as a whole, you use the plural form without an apostrophe:"The Smiths are hosting a party."

So, your invitation should read:"Hosted by The Smiths"