In Season 6, Episode 2 of Game of Thrones, Balon Greyjoy remarks to Asha that he is the last surviving king from the original five. The deaths of Renly, Joffrey, and Robb are all known throughout the kingdom at this point, but how he does he know of Stannis' death?
Although it's not quite clear how much time passed between seasons 5 and 6, it's seems like it's only been but a few days. Brienne is still outside of Winterfell at the beginning of Season 6 and it's doubtful she would have spent much time outside of Winterfell, waiting in the cold. If the events at Castle Black share the same timeline, then that will also confirm it's only been 1 - 2 days.
Meanwhile, the isle of Pike is hundreds of miles away and the few Iron Islanders that remain on the mainland are located on the coast. It's quite close to winter, meaning few people still travel outside of the keeps. It's even less likely that one of the northerners at Winterfell would travel to the coast and talk to the Iron Islanders. The only other option is a raven, but not a single other person outside of Winterfell has brought up Stannis and Balon Greyjoy seems like the last person Ramsay would notify.