The story of Saints Joachim and Anne is not recorded in Scripture but has an ancient and venerable history from the earliest days of Christianity. It is related in a format similar to the Old Testament accounts of miraculous conceptions and births: Anne is "barren" (this devout married couple were unable to have children), but both husband and wife prayed for a child, and God made fruitful their conjugal union and blessed them with a child who would play a crucial role in the history of salvation.
But as we know from our faith, there is so much more to this event than any comparable stories about the births of patriarchs and prophets. The child conceived in Saint Anne's womb is destined to be the mother of the Savior, the all-holy and immaculate Mother of God. Thus, these persons - Mary's parents - are precious, and their story is held in great esteem (even though its primary source that we know of is an Apocryphal Gospel). It was in the context of their conjugal self-giving love that God began His definitive "entrance" into history, not only by making the couple fruitful, but also by preserving their child Mary from original sin from the first moment of her conception.
Mary's conception was "the beginning" of something radically new. Perhaps we might say it was in some sense the "beginning" of the New Creation. Mary was the Woman who was prepared entirely to receive - with complete and personal freedom - the incarnate Word, and accompany Him throughout His life, His ministry, His crucifixion and resurrection (the redeeming effects of which applied to her "in advance" - according to the way time unfolds for creatures in this present age), His Ascension, the Gift of the Spirit and the birth of the Church at Pentecost, and her own "Dormition"/Assumption into the fullness of her Son's bodily resurrected life. It is not surprising, therefore, that from the beginning of Christian history attention was given to human historical moment in which God created the All-Holy Ever-Virgin Mary, Mother of God.
Mary's parents were clearly prepared by extraordinary graces to become - really, truly - her father and mother. Theirs were the first human faces that looked upon and loved the woman chosen to be the Theotokos. How awesome it must have been to be entrusted with so singular a gift (even if they were not yet aware of her unique vocation). Was there perhaps an inkling in their hearts, even when they held their little Mary as a baby? Such a special joy would be appropriate for Joachim and Anne, just as some echo of this joy is experienced in the sense of wonder that fills the hearts of every mother and father when they gaze upon the new human person that has been entrusted to their love and care.
There is no tradition (that I'm aware of) of referring to these saints as the "Grandfather and Grandmother of God," nor what theological relevance that would have for us. But the Person who was their grandson was God, the only-begotten Son of the Father. I'm not certain they lived to see his birth. Scripture is entirely silent on any of these details. No matter what, however, their lives were greatly blessed, and the purity of their hearts was abundantly rewarded.
Saint John Damascene (8th century) has some helpful reflections for today's feast day in honor of Saints Joachim and Anne, from a sermon which is presented in part in today's Liturgy of the Hours, in the "Office of Readings":
"Anne was to be the mother of the Virgin Mother of God, and hence nature did not dare to anticipate the flowering of grace. Thus nature remained sterile, until grace produced its fruit. For she who was to be born had to be a first born daughter, since she would be the mother of the first-born of all creation, in whom all things are held together.
"Joachim and Anne, how blessed a couple! All creation is indebted to you. For at your hands the Creator was offered a gift excelling all other gifts: a chaste mother, who alone was worthy of him.
"And so rejoice, Anne, that you were sterile and have not borne children; break forth into shouts, you who have not given birth. Rejoice, Joachim, because from your daughter a child is born for us, a son is given us, whose name is Messenger of great counsel and universal salvation, mighty God. For this child is God.
"Joachim and Anne, how blessed and spotless a couple! You will be known by the fruit you have borne, as the Lord says: By their fruits you will know them. The conduct of your life pleased God and was worthy of your daughter. For by the chaste and holy life you led together, you have fashioned a jewel of virginity: she who remained a virgin before, during and after giving birth. She alone for all time would maintain her virginity in mind and soul as well as in body.
"Joachim and Anne, how chaste a couple! While safeguarding the chastity prescribed by the law of nature, you achieved with God’s help something which transcends nature in giving the world the Virgin Mother of God as your daughter. While leading a devout and holy life in your human nature, you gave birth to a daughter nobler than the angels, whose queen she now is.
"Girl of utter beauty and delight, daughter of Adam and mother of God, blessed the loins and blessed the womb from which you come! Blessed the arms that carried you, and blessed your parents’ lips, which you were allowed to cover with chaste kisses, ever maintaining your virginity. Rejoice in God, all the earth. Sing, exult and sing hymns. Raise your voice, raise it and do not be afraid."