Hmm I reading it again and looking up the commentary for Matthew 19, a case could be made I think that there too, the phrase refers to the “putting away”… Which would be like a separation according to Catholic teaching, which is permitted in cases. In the early Church it seems they used the word “divorce” for this too as for anulments.
Haydock Commentary, Matthew 19
Ver. 9. And I say to you. It is worthy of remark, that in the parallel texts, St. Mark x. 2. and St. Luke xvi. 18. and St. Paul to Corinthians vii. 10. omit the exception of fornication; and also that St. Matthew himself omits it in the second part of the verse; and says absolutely, that he who shall marry her that is put away committeth adultery. It perhaps crept in here from chap. v. 32, where it is found in a phrase very similar to this, but which expresses a case widely different. Divorce is in no case admitted but in that of adultery. This is what Christ teaches in chap. v. 32, and to this the exception is referred, marked in the two texts. But in this very case the separated parties cannot contract a second marriage without again committing adultery, as we must infer, from a comparison of this text with the parallel texts of St. Mark and St. Luke. (Bible de Vence)
— If we did not understand it in this manner, the case of the adulteress would be preferable to the case of her who should be put away without any crime of her own; as in this supposition, the former would be allowed to marry again, which the latter would not be allowed. (Tirinus)
— St. Augustine is very explicit on this subject. See lib. 11. de adult conjug. chap. xxi. xxii. xxiv.
— St. Jerome, in his high commendation of the noble matron, Fabiola, says of her: “that though she was the innocent party, for the unlawful act of marrying again, she did public penance.” (In Epitaph. Fabiolæ.)
— This universally received doctrine of the Catholic Church was confirmed in the general council of Trent. (Session xxiv. canon 6.)