The third paragraph in my previous reply is in fact about printing from an iPhone, but that would be via the Canon PRINT app, which I guess is the one that you are using already.
The fourth paragraph is about a Raspberry Pi print server. Once such a print server has been set up, it should be possible to use it in connection with a printer, also for printing from an iPhone without an iOS app. However, the print server uses Linux, and its printing system (CUPS) would have to be able to find an appropriate way of working with the G3416, which is not certain in this very case. That would make it entirely experimental.
It may be easier to look for another printer with built-in AirPrint support (see the list in About AirPrint - Apple Support).