According to paedobaptists, what justifies a link between circumcision and baptism since both males and females are baptised?

You could easily ask what the link between Baptism and the Baptismal offices of Priest, Prophet and King.

• In the Jewish tradition the Levitical priesthood was reserved to firstborn sons

  But in the Christian tradition, all sons and daughters are Baptized into the office of a universal priesthood; only some are called to a sacerdotal priesthood - but it has nothing to do with lineage.

• In the Jewish tradition, prophets were anointed or specifically called by God, the prophets were mostly male, but there were some female prophets - in the Bible, there were probably many more not recorded.

  In the Christian tradition, prophecy is a gift that strikes where the Holy Spirit needs it. The gift of prophecy is irrespective of sex. But the office of prophet, under Baptism is afforded to all.

• In the Jewish tradition, kings were men because that's a title given to men. Kings were also only reluctantly chosen and they were first chosen among those anointed by prophets.

  In the Christian tradition, men and women are given a share of the office of King, but the Kingdom is not of this world.

Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death?

No, me neither, I don't think I'm dead. So what are you getting at St. Paul? Are you saying that Baptism is a spiritual sign made physically present (i.e. a Sacrament)?

This is all not to say that there aren't sacraments that paedobaptists will also don only upon men, (i.e. Holy Orders).

Circumcision was important to Jews, but St. Paul and reluctantly St. Peter, realized that Christians are not Jews and there are certain things we have to make up as we go along and trust to the Holy Spirit that we're not wrong with. Just as good parents will have to "pick their battles" with teenagers, the Apostolic Fathers couldn't continue Jewish dietary or circumcision practices and hope to reach the gentiles. So they did what Jesus did in His preaching, they extended the Old Law to be universal and spiritual. Which is why everyone needs circumcision now, but nobody needs a knife.

Going off my answer to What is the basis for Lombard's view that the basis of justification for OT men was different than for OT women?

Q: Why are female babies baptized if they were not circumcized?

A: Because circumcision was an imperfect, legal prescript of the Old Law. Baptism is perfect, and part of the New Law brought about by Christ.

It was imperfect...

Now in comparison with baptism, circumcision was imperfect in three ways. First, as to its signification, for it did not signify so explicitly the cleansing of the whole man from the uncleanness of all of original sin, as the washing of baptism does. Second, as to its efficacy, for the grace that was given in circumcision was not so abundant for working virtuously and for repressing the kindling of sin as it is in baptism. Third, as to benefit, for its benefit was not as widespread as baptism’s, since it had a particular people, a particular sex, and a particular time, which does not happen in baptism; and thus, once the time of fullness arrived, circumcision had to end, to be replaced by baptism.

cf:

Only Men: St. Thomas, arguing against the notion that women should have had circumcision (or some equivalent remedy), quotes Hugh of St. Victor in saying

the circumcision of the flesh was given to men alone, for the Sacred Scriptures customarily represented the soul by the masculine sex, but the flesh by the feminine, so that it would be manifest that circumcision conferred sanctification on souls, but did not remove the corruption of the flesh. _{(Aquinas, Sentences IV, D. 1 Q. 2 A. 2.2.SC)}

Consider:

For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus. And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise.
— Galatians 3:27–29

• Judaism is God's law practiced at a physical level.
  Circumcision is a token or sign of God's covenant with Abraham and his descendants, "between me and you and thy seed after thee" (Genesis 17:10–11).
• Christianity is God's law practiced at a spiritual level.
  Infant baptism is a token or sign of God's covenant with Christians, "all baptized into one body" (1 Cor 12:13).

At the physical level, descent was recorded by male ancestry.
At the spiritual level, one's sex is irrelevant, as is one's ancestry or social position.

OP: Given that no female babies were circumcised as a sign of the Abrahamic covenant, why are female babies of Christian believers given the sign of the new covenant (water baptism)?

To find an answer to your excellent question, I turned to some earlier Christians like Tertullian and Aquinas for some light.

To bolster the following explanation, one could have also asked, circumcision was given to the male Israelites, that particular one nation, yet baptism is for all nations (Mat 28:19).

It might be an interesting question, but I've no idea who first formally associated (incorrectly?) the two signs of circumcision and water baptism. There appears only to be an assumption that the signs refer to the same thing.

This is from a book quoted in the OP, emphasis mine.

“The children of believers continue to have the same special relationship to the covenant as their Old Testament counterparts had; and, consequently, the same right to the covenant sign. Why do I baptise children? ...It is because God gave me an ordinance: Put the sign of the spiritual covenant on the physical seed.”

It appears assumed that the covenant sign of circumcision somehow finds its identity in another covenant sign baptism. But, as the OP says, "There seems to be something out of sync with this claimed link." Indeed, and again, one may wonder why to a nation versus all nations.

Aquinas outlines circumcision's reason and purpose.

The institution of circumcision is as a sign of Abraham's faith, who believed that himself would be the father of Christ Who was promised to him: and for this reason it was suitable that it should be for males only. Again, original sin, against which circumcision was specially ordained, is contracted from the father, not from the mother, as was stated in the FS, Q[81], Aquinas ST 70.2

Is that a loaded statement or what? Anyway, circumcision was essentially a sign of the Saviour! Here is the OT quote and the NT mention.

And I will establish my covenant between me and thee [Abram] and thy seed [singular Gal 3:16] after thee in their generations for an everlasting covenant, to be a God unto thee, and to thy seed after thee. Gen 17:7

Given the point of circumcision, the seed pointing to Christ, where does baptism fit?

And were all baptized unto Moses in the cloud and in the sea; 1 Cor 10:2

Christian baptism is foreshadowed under the Red Sea crossing during the Exodus. Passover was redemption. The cloud (and fire) represents the Holy Spirit who show up prior to the sea (recall Cornelius receiving the Spirit prior to baptism). The sea was sealing/protecting (with the potential of a kingdom of priests and kings).

Thus, ALL, not just the men, not just the Israelites (Ex 12:38), were saved out of Egypt, led by the Spirt, and baptized in water.