When does Babushka bring the gifts?

Answer 1

She doesn't. The so-called Babushka is the product of imagination of an American poetess Edith M. Thomas who in 1907 wrote a poem Babushka: a Russian Legend. In Russia, nobody has ever heard about the gift-giving Babushka and this character doesn't exist in the Russian folklore at all. In Russia, it's Father Frost who brings gifts to children and adults on New Year's Eve. This Babushka thing is just a sick joke. She doesn't exist in Russia, period.

Answer 2

Babushka is a figure from Russian folklore who traditionally brings gifts to children on New Year's Eve, not Christmas. In some traditions, she may also bring gifts on the Epiphany or Russian Christmas, which falls on January 7th.