Why does anyone need to convince someone of simple statement of facts?
Besides, either one believes Jesus is God or not ("is" includes that Man is and will remain God too). The title [for Mary] is then academic because it is a simple statement of the belief just stated - that He is God.
Mary gave birth to a man Who was also the Son of God. So properly speaking, Mary is properly called the Mother of God from that point forward because of Who she gave birth to - not because of something Divine about Her but because He is Divine.
The rebuttal that in Heaven she is somehow is no longer the woman that gave birth to that Man (the point of the title Mother of God) after Mary left this earth fails; just as the idea no one has any of the familial relationships they had on earth in Heaven fails. Jesus is still a human, glorified yes, but still human with a body and soul. Humans have mothers, Mary is His and she is still His Mother now. That Man is also will always be God. So calling Her Mother of God now is simply a title that reflects the same truth it would have reflected had that title been used while Mary walked this earth - it is still not about who Mary is - it is reflection on Who Her Son is, God.
The rebuttal that using that title reflects a belief that Mary in Heaven now is somehow Divine or participated in the "creation" of God is absurd as the Creeds of the same people using that title deny God (Father, Son and Holy Spirit) is created. Those declarations are made by Catholics daily 24/7/365. So it would be rather silly to suggest people using that title somehow are saying Mary is Divine or Mary help "create" God when the people using that title know and repeatedly proclaim God is uncreated. Similarly calling Her Mother of the Church reflects a deeper reflection of the act/scene described at the Cross and so Mary could properly be called Our Mother too as members of that Church, but using that title does NOT indicate a belief she gave birth to all of us, anymore than calling Her Mother of God would indicate a belief that She created God in Her womb or is somehow Divine herself.