She does not remember whether she made up the days that she owed or not

You do not have to make them up; it is sufficient for you to act upon what you think is most likely. 

Acting on the basis of what you think most likely with regard to acts of worship is something that was narrated in sharee’ah. For example, the Prophet (peace and blessings of Allah be upon him) said: “If any one of you is uncertain about his prayer (i.e., how many rak’ahs he has prayed), let him think what is most likely to be the case and complete the prayer on that basis, then say the tasleem, then prostrate twice.” Narrated by al-Bukhari, 401; Muslim, 572. 

Al-Nawawi said: 

This is evidence (that supports the view of) Abu Haneefah – may Allah have mercy on him – and those who agreed with him among the people of Kufa and others of ahl al-ra’y, that whoever is uncertain of how many rak’ahs he has done in his prayer should act on the basis of what he thinks is most likely to be the case; he does not have to limit himself to the lower amount and do more. The apparent meaning of this hadith is their evidence. End quote. 

Shaykh al-Islam confirmed in Majmoo’ al-Fatawa (23/5-16) that this hadith refers to acting upon what one thinks is most likely the case. He regarded as weak the view of some scholars, that what is meant by acting upon what one is certain of is to act upon the smaller number, such as if a person is unsure as to whether he has prayed two rak’ahs or three, he should assume it is two. 

Shaykh Ibn ‘Uthaymeen said in his book Manzoomaat fi Qawaa’id al-Fiqh wa Usoolihi: 

If you cannot be certain, than refer to what you think is most likely to be the case, then you will be following the right course. 

What this means is that if a person cannot act on the basis of certainty, then he should act on the basis of what he thinks is most likely the case. 

If you think it is most likely that you made up those days, then you do not have to do anything; you do not have to make up these days again. 

If a woman is not sure whether she made up the days that she owes or not, and neither seems more likely to her to be the case, then she has to make them up. 

Shaykh Ibn ‘Uthaymeen was asked in Fataawa al-Siyaam (p. 372): If a woman does not fast some days in Ramadaan, but she forget whether she fasted those days or not, and all she remembers is that she only has one day left, should she fast those days again or act on the basis of what she is certain about? 

He replied: 

If she is not certain that she has one day left, then she only has to fast one day, but if she is certain that she only has to fast one day, but she is not sure whether she fasted it or not, then she has to fast it, because the basic principle is that she still owes it, and if she has not discharged her duty then she still has to fast it. This is unlike the case of one who is uncertain as to whether she has one day or two to fast; she only has to fast one day. But if she knows that she has to fast one or more days, but she is not sure whether she fasted them or not, then she has to fast it, because the basic principle is that she still has to fast it.