The husband may take back his wife whom he divorced revocably during the ‘iddah, and it is not stipulated that she should be present or know of it, or that the taking back be done in the presence of a notary, whether the divorce was issued in the presence of a notary or not.
But it is mustahabb for the taking back to be witnessed by two witnesses, and it was said that it is obligatory for it to be witnessed.
Ibn Qudaamah (may Allah have mercy on him) said: Taking back is done by saying to two Muslim men: Bear witness that I have taken aback my wife, without any guardian being present and without any mahr being added. Another report was narrated from Abu ‘Abdullah (may Allah have mercy on him), which says that it is permissible to take the wife back without it being witnessed, the reason being that taking back does not require any guardian or mahr, or the consent or knowledge of the wife, according to scholarly consensus, because of what we have mentioned about the woman who us revocably divorced coming under the heading of rulings on wives, and taking her back means keeping her and continuing marriage to her. Hence Allah, may He be glorified and exalted, described taking back as “retaining” and leaving them as “releasing” them, as He says (interpretation of the meaning): “…and they have reached their term, then retain them in kindness or release them in kindness” [al-Baqarah 2:231] and, in another verse, “and then (a woman) must be retained in honour or released in kindness” [al-Baqarah 2:229]. Marriage is broken by divorce and is restored when the divorce is rendered null and void; taking back the wife removes the reason for the break and stops it going all the way to irrevocable divorce; therefore it does not require what is required to initiate a new marriage contract.
With regard to witnessing, there are two reports, one of which says that it is obligatory. This is one of the two views of ash-Shaafa‘i, because Allah, may He be exalted, says (interpretation of the meaning): “Then when they are about to fulfil their term appointed, either take them back in a good manner or part with them in a good manner. And take for witness two just persons from among you (Muslims)” [at-Talaaq 65:2]. The apparent meaning of the command is that it is obligatory, and because this is for the purpose of making intimacy permissible, having it witnessed is required as in the case of the marriage contract.
The second report says that having witnesses is not required. This is the view favoured by Abu Bakr, and was the opinion of Maalik and Abu Haneefah, because there is no need for acceptance, so there is no need for witnesses, as is the case with all the husband’s rights, and that is because with regard to that in which the guardian’s consent is not required, it is not necessary to have witnesses. In this case the command is understood as meaning that it is mustahabb. However there is no difference of opinion among the scholars that it is Sunnah to have witnesses.
End quote from al-Mughni, 7/403
Thus you know that your husband may have taken back during the ‘iddah and that his taking back is valid, whether he took you back in the presence of a notary or not. But if he comes after the end of your ‘iddah and claims that he took you back, he will be to provide proof, which is the testimony of two witnesses, unless you believe his claim, in which case you may go back to him.
If the woman gets married after the end of her ‘iddah, then her first husband claims that he took her back without her knowledge and provides proof of that, then she is to be returned to him.
Ibn Qudaamah (may Allah have mercy on him) said: If the husband of the revocably divorced woman takes her back without her knowledge, that taking back is valid, because it does not require her consent and therefore it does not require her knowledge either, as in the case of talaaq. If he took her back and she did not know, then her ‘iddah ended and she married someone else, then he comes and claims that he took her back before her ‘iddah ended, and he has proof of that, it is proven that she is his wife and the second marriage is invalid, because he (the second husband) married the wife of another man. So she is to be returned to the first husband, whether the second husband consummated the marriage with her or not. This is the correct opinion and it is the view of most of the fuqaha’, including ath-Thawri, ash-Shaafa‘i, Abu ‘Ubayd, and ashaab ar-ra’y. It was also narrated from ‘Ali (may Allah be pleased with him).
A second report was narrated from Abu ‘Abdillah (may Allah have mercy on him): if the second husband has consummated the marriage with her, then she is his wife and the first marriage becomes invalid. This was narrated from ‘Umar ibn al-Khattaab (may Allah be pleased with him), and it is also the view of Maalik. Something similar was narrated from Sa‘eed ibn al-Musayyab, ‘Abd ar-Rahmaan ibn al-Qaasim and Naafi‘. End quote from al-Mughni, 7/411
Based on that, perhaps you can consult a lawyer to see whether it is possible to reopen the case of khula‘ easily after it was closed, or whether it is possible to leave it without closing it. Or you can try to find out your husband’s attitude by any means, so that you can find out whether he took him back before the end of your ‘iddah or not, so as to know exactly where you stand.
We ask Allah to make things easy for you and to decree good for you wherever it may be.
And Allah knows best.