Of all the spurious letters from Ignatius, I doubt his letters to either John the apostle or Mary were even written by a believer. This does produce a lot of ideas that became the Mariology of the RC church today, but certainly John nor Mary would approve of these letters. Even if Mary was always a virgin, and even if she was sinless, still, nobody should talk about her the way the false Ignatius talks about her in his first epistle to John. If I was Mary and/or John, I would get a restraining order on the members of the Syrian church.
Pseudo-Ig writes another letter to John, this time going on and on about how much James looks like Jesus. This is still under the mentality that Mary was always a virgin and adopted Jesus's brothers. If James really did look like Jesus, then that is proof in itself that he really is the son of Mary and Joseph. Mary cannot be both sinless and a perpetual virgin b/c the Bible says she was married. Marriage is more than sex but it is not less. If she was always a virgin then she was not married, but she was married, so she had the proper relations with Joseph. It was only when she gave birth to Jesus that she had to be a virgin. He was conceived without two sinful parents, and he was still fully human with Mary's DNA.
Sidebar: why then did Jesus give John to Mary as her son at the cross? At that time, none of Jesus's biological siblings were Christians. James and Jude became Christians later, but John and Mary were now kin since Jesus completed his sacrifice and earthly mission.
The letter Pseudo-Ig wrote to Mary is not too noteworthy. What is noteworthy is the reply supposedly from Mary. I dare say, Ignatius did not write these letters nor anybody who could call himself a believer. If, however, Mary lived at the time this letter was written, I believe she and John would definitely agree to its contents.
Mary reminds Ignatius that she is only Christ's handmaiden. She bore his body, but he is still her God and Savior, and Mary takes her proper position as a godly woman who said yes and who became the first true Christian, the first example of what all the Church is. Then she tells him that all John wrote in his gospel about Jesus is true. Listen to those words. She does what all true believers do in pointing to Jesus, showing him exalted, taking the attention off of herself, and even saying that Jesus exalted himself and John's accounting of that is true. She says, "I obeyed God, and he blessed me, but I am no different than the rest of you. Jesus alone is your redemptor, and I look to him for my justification."