I'm guessing you are not logged on to a wifi router or network. Since the smart controller is not a cellular device you need to either be logged onto your home wifi network, or setup your phone as a hotspot and log the wifi onto that connection. obviously you need to have the wifi turned on in the Smart Controller as well. That is the only reason it would say "check your internet connection" that I can think of.
I was logged into WIFI and Bluetooth and couldn't login. It was so frustrating because I had a job that afternoon and it would only let me fly up to 96ft without being logged in.
So I just started pushing the buttons on the screen trying to login over and over and it finally logged in. This is AMAZINGLY POOR ENGINEERING. I'm so tired of DJI, I would love to get into American drones if there are any comparable out there.
Unfortunately, I don't have a solution for when this happens to people. This is what happens when you use Chinese ingenuity for another country (USA). It doesn't work so well.