Verizon LG G2: Not unique to G2, but...

[iLLy33]

Receive a notification randomly, black rectangular box, "You have internet connection" happened on Motorola device also, obviously an app but wondered if anyone else has seen this.

 

[srkmagnus]

Receive a notification randomly, black rectangular box, "You have internet connection" happened on Motorola device also, obviously an app but wondered if anyone else has seen this.

I haven't seen this on any of my devices. Or at least have not noticed it. Do you recall enabling a setting to inform of a data connection? Check system settings > mobile networks.