You clearly know few people who come to this country to settle here.  I have known very many over many years, and I have heard none of them talking to Americans about anything that would remotely demonstrate a lack of gratitude for the opportunity to be here.  
Many people do find our customs strange and our language difficult to learn.  Nevertheless, they adapt, and their children become as American as anyone else.
I don't know if you have any concept of how difficult it is to leave one's home and everything familiar in order to find safety or to be able to provide for one's family.  If the trauma that the immigrants suffer manifests itself in ways that offend you, then I am sorry for you.
If one is to speak about being ungrateful and unappreciative, I would use native-born Americans as a prime example.  Close to a majority of them choose not to vote; many cheat on taxes.  That, to me is far greater evidence of a lack of gratitude than anything any immigrant might say.