What significance do Catholics see in the fact that Adam and Eve 'knew each other' only after original sin? From a Catholic perspective, what can be said about the fact that Adam and Eve 'knew each other' only after original sin?
St. Thomas Aquinas's Summa Theologica question "Whether in the state of innocence there would have been generation by coition?" sheds some light on this. St. Thomas quotes a chapter of Gregory of Nyssa entitled "What we must answer to those who raise the question—'If procreation is after sin, how would souls have come into being if the first of mankind had remained sinless?'," who


  says (De Hom. Opif. [On the Making of Man] xvii) that in paradise the human race would have been multiplied by some other means, as the angels were multiplied without coition by the operation of the Divine Power. He adds that God made man male and female before sin, because He foreknew the mode of generation which would take place after sin, which He foresaw.


Yet, according to St. Thomas, "this is unreasonable" because


  what is natural to man was neither acquired nor forfeited by sin. Now it is clear that generation by coition is natural to man by reason of his animal life, which he possessed even before sin, as above explained (Question [97], Article [3]), just as it is natural to other perfect animals, as the corporeal members make it clear. So we cannot allow that these members would not have had a natural use, as other members had, before sin.


St. Thomas also quotes St. Augustine's De Civ. Dei [City of God] xiv, 26:


  We must be far from supposing that offspring could not be begotten without concupiscence. All the bodily members would have been equally moved by the will, without ardent or wanton incentive, with calmness of soul and body.


Thus, there is nothing sinful about sexual intercourse itself, nor is it the result of sin.

More to the point of your question is the objection St. Thomas poses in the same article:


  Objection 2: Further, our first parents were created at the age of perfect development. Therefore, if generation by coition had existed before sin, they would have had intercourse while still in paradise: which was not the case according to Scripture (Gn. 4:1 ["…Adam knew Eve his wife…" after the fall]).


to which he replies with St. Augustine's opinion:


  Augustine says (Gen. ad lit. [Literal Interpretation of Genesis] ix, 4), our first parents did not come together in paradise, because on account of sin they were ejected from paradise shortly after the creation of the woman; or because, having received the general Divine command relative to generation, they awaited the special command relative to time.


Here's the original Latin of St. Augustine with the translations from here:


  Quare primi parentes in paradiso non coierint.[Why was there no nuptial union in Paradise?]
  
  Cur ergo non coierunt, nisi cum exiissent de paradiso? Cito responderi potest: Quia mox creata muliere, prius quam coirent, facta est illa transgressio, cuius merito in mortem destinati, etiam de loco illius felicitatis exierunt. Non enim Scriptura tempus expressit, quantum interfuerit inter eos factos, et ex eis natum Cain.[Why, then, did they not have intercourse until they had left Paradise? The reason is that soon after the creation of the woman, before they had relations, they committed the sin because of which they were destined to die and because of which they went forth from the place of their blessedness. As a matter of fact, Scripture has not specified the length of time between their creation and the birth of their son Cain.]
  
  Potest etiam dici quia nondum Deus iusserat ut coirent. Cur enim non ad hanc rem divina exspectaretur auctoritas, ubi nulla concupiscentia tamquam stimulus inobedientis carnis urgebat? Ideo autem hoc non iusserat Deus, quia secundum suam praescientiam disponebat omnia, in qua et eorum casum procul dubio praesciebat, unde iam mortale genus propagandum esset humanum.[One might also say that the delay was due to the fact that God had not yet ordered them to come together in nuptial union. For why should they not await God's authorization for this, since there was no drive of concupiscence coming from rebellious flesh? God had not ordered such a union because He provided for everything in the light of His foreknowledge, in which He undoubtedly foresaw their fall, as a result of which the human race was to be generated as a mortal race.²²]²²[Translator's note: "I understand mortale as a predicate adjective referring back to genus humanum."]