If male cousins say Salaam, should the female respond?

Answer

It is not permissible to greet a ghair mahram. Neither should a man greet a woman nor vice versa. While this is unmannerly according to kuffaar culture, it is honourable and respectable in terms of Islam. Do not greet or respond to the salaam of a male cousin. Don't be concerned with his annoyance. Be concerned with Allah's Pleasure and Displeasure.