That’s an interesting Scripture. To me the author seems to be making a comparison of how the earthly temple holy things was dedicated or consecrated with the blood of animals, compared with the heavenly temple, the true temple, not a copy, is consecrated through the blood of Christ. In the first case the blood sacrifice is to make a covenant with Moses, the people to God to obey the commandments. In the second case a covenant is made between heaven itself, the Father and the the Son (Mediator) which redeems mankind. And thus it could be that the author sees heaven itself as being consecrated with blood as part of this covenant process, just like in the first case.
Here is Navarre commentary
The text might seem to be saying that the heavenly sanctuary, like the Mosaic sanctuary, also needs purification. However, it is impossible for heavenly things to need purification from any stain or imperfection. This has led to many different interpretations being offered to explain what the purification mentioned here means. Some have seen the “heavenly things” as referring to the Church on earth, an as yet imperfect image of the Church in heaven and still in need of purification. Others see them as referring to the Church in heaven, the Church triumphant, in the sense that it has to purify sinners so as to be able to receive them into its bosom and destroy the roots of evil. St Thomas interprets the text as referring to the abolition of impediments to entry to the sanctuary. Men need to be purified of sin in order to enter heaven.
The words “heavenly things” seem to refer to the dedication or inauguration of heaven—conceived as a sanctuary, where God has his dwelling-place—with the blood of Christ. The old sanctuary was inaugurated and dedicated by a large number of blood sacrifices (cf. 1 Kings 8:62–64; 1 Mac 4:52–56). The new worship in the heavenly sanctuary cannot begin without the shedding of Christ’s blood. Although the Christian has access to the sanctuary which Christ has inaugurated, he needs to remember that because it is so great and so perfect he cannot enter it if he has any stain or imperfection. Therefore, God has established that the souls of those who die in his friendship but who are not completely free from venial sin, are to be cleansed in purgatory. “To that [the beatific] vision no rational creature can be elevated unless it be thoroughly and entirely purified …]. But it does at times happen that such purification is not entirely perfected in this life; one remains a debtor for the punishment …]. Nevertheless, he is not entirely cut off from the reward, because such things can happen without mortal sin, which alone takes away the charity to which the reward of eternal life is due …]. They must, then, be purged after this life before they achieve the final reward” (St Thomas Aquinas, Summa contra gentiles, 4, 91, 6).