Answered by Shaykh Amjad Rasheed
My husband divorced me a non-finalized divorce on September 9, 2004, and gave me the option to either come back to him within a month, or within three months after a new marriage contract.

First, a non-finalized divorce is when a man pronounces fewer than three divorces on his wife with whom he has had sexual intercourse, and there is no compensation. If he has not had sexual intercourse with her, then the divorce is finalized and there is no waiting period. If they want to return to the marriage, they’ll have to do a new contract.
If he has divorced her three times, the woman is not lawful for him until she marries someone else. If the divorce was for some type of compensation, then it is a khul’ [another type of divorce] and it is final and has no waiting period. There is no getting back together except with a new contract.
Second, to take back a wife after a divorce is a right of the husband. If he wants to take her back, he has to effect it by saying “I take you back” or something similar which has the same meaning. It is not valid to make [his taking her back] contingent on the wife’s wishes or anyone else’s. So your decision to go back to him does not have any effect even if it took place within the aforementioned one-month period.
Third, the duration of the waiting period is a Sharia’ law. Neither the husband nor anyone else has the authority to change that. Therefore, if the inquirer is still in the category of menstruating women, then her waiting period is three consecutive intervals of purity. If she is past menstruation or does not menstruate, her waiting period is three months. If she is pregnant, her waiting period is until she delivers her baby. So the divorcing husband is allowed to take back his divorced wife [anytime] during this waiting period without a new contract, whether or not the stipulated one month is over. [What’s important is] as long as you are in your waiting period.
Fourth, the presence of the wife or witnesses is not a condition for the validity of his taking her back. It is enough for the husband to pronounce the aforementioned [“I take you back.”], even if he is alone.
Amjad Rasheed
[Translated by Zaynab Ansari]