The news site said Wellington man Michael Carey was angry about the leaflet, which his children had found in the letter box. He believed it put New Zealand on a "dangerous slippery slope" in comparison with the United States.
David Tipple, the owner of the chain which has stores in Auckland, Wellington, Christchurch and Hamilton, defended the ad.
Keegan MacPherson-Pirini, 12, died in 2014 after an air rifle went off by accident at his Pongakawa Bush Rd home near Te Puke. The pellet went through his heart.
Keegan's father Jayson Pirini told stuff.co.nz that air rifles were not appropriate for children.
They were powerful and should be treated "like a normal gun".