assalam 'alaikum warahmatullahi wabarakatuh

Sister that is not a bad title I am sure for an important question. I am not a scholar so I cannot give you any Fatwa on these isuues. Therefore I have searched for a Fatwa of an 'Ulama about it. Finally I am able to find it for you and all the brothers and sisters over here.
Here is the Fatwa of Sheikh al-'Uthaimeen (may Allah have mercy on him).
I forgot that I did not have wudoo’ and I prayed. After I finished my prayer, I remembered that. Do I have to repeat my prayer?
Praise be to Allaah.
Yes, whoever prays forgetting that he does not have wudoo’ has to repeat the prayer, because the Messenger (peace and blessings of Allaah be upon him) said: “Allaah does not accept any prayer if a person breaks his wudoo’, until he does wudoo’.” (Narrated by al-Bukhaari from the hadeeth of Abu Hurayrah (may Allaah be pleased with him) in Kitaab al-Wudoo’. This is in contrast to the person who has some impurity (najaasah) on his clothes and he forgets it. He does not have to repeat his prayer because Jibreel came to the Prophet (peace and blessings of Allaah be upon him) whilst he was praying, and told him that there was something dirty on his shoes. He took them off and continued praying. This was narrated by Ahmad from the hadeeth of Abu Sa’eed al-Khudri (may Allaah be pleased with him) in his Musnad. This hadeeth proves that the one who is unaware of the najaasah does not have to repeat his prayer, and this applies also to the one who forgets that there is some najaasah present.
I’laam al-Musaafireen bi Ba’d Aadaab wa Ahkaam al-Safar wa ma yakhuss al-Mallaaheen al-Jawwiyyeen by Shaykh Muhammad ibn Saalih al-‘Uthaymeen, p. 12
Also here follows what is provided in Islam QA.
Sometimes after prayers I remember that I had not gone through 'woudou'. Again, should I do my woudou and pray again?.
Praise be to Allaah.
Yes, you have to do wudoo’ and repeat your prayer. The scholars are unanimously agreed on that, because purity (tahaarah) is one of the conditions of prayer being valid. The evidence for that is the words of the Prophet (peace and blessings of Allaah be upon him): “Allaah does not accept the prayer of any of you if he breaks his wudoo’, unless he does wudoo’ again.” Narrated by al-Bukhaari, 6954; Muslim, 225.
Muslim (224) narrated that ‘Abd-Allaah ibn ‘Umar said: I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “No prayer is accepted without purification.”
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’, 2/79:
The Muslims are unanimously agreed that it is haraam for a person who has broken his wudoo’ to pray, and they are unanimously agreed that his prayer is not valid, whether he is aware that he broke his wudoo’ or is unaware of that or forgot. But if he prayed because he was unaware of it or forgot, then there is no sin on him, but if he was aware that he had broken his wudoo’ and that it was haraam for him to pray in this situation, then he has committed a grave sin.
And Allaah knows best.
Islam Q&A
:salam2: sister, hope ya doing well. sister Allah will not punish His servant for what they forgot. If you didn't do it in purpose. You don have to repeat your Salaat as far as my understanding. if you remembered in the middle of salaat you may have to repeat the prayer. Allah knows best
wa'alaikumussalam warahmatullahi wabarakatuh
:astag:Fear Allah my dear sister.
Hope this helps on the topic.
wassalam 'alaikum warahmatullahi wabarakatuh